中国大学Engineering Mechanics期末答案(慕课2023课后作业答案)

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01 Reductions of force systems

Tests for week 1

1、中国作业As shown in the parallelogram,大学答案答案 all forces are at point A. In which figure FR can be considered as the resultant of F1 and F2?
A、
B、期末
C、慕课
D、课后

2、中国作业Neglect the weights of all members. In which case bar BD is 大学答案答案not a two-force member?
A、
B、期末
C、慕课
D、课后

3、中国作业To study the whole system,大学答案答案 which free-body diagram is correct?
A、
B、期末
C、慕课
D、课后

4、To study the whole system, which free-body diagram is correct?
A、
B、
C、
D、

5、To study the whole system, which free-body diagram is correct?
A、
B、
C、
D、

6、For bar AD, which free-body diagram is correct?
A、
B、
C、
D、

7、In this equilibrium mechanism, the free-body diagram of crank OA can be drawn as
A、
B、
C、
D、

8、The resultant force of two intersecting forces and is , i.e., . The magnitude of must be larger than those of and .

9、As long as two forces have the same magnitude and are in opposite directions, these two forces form a couple.

10、For any coplanar force system, as long as its principal vector is not equal to zero, the force system can be reduced to one single force.

02 Equilibrium of force systems

Tests for week 2

1、All weights and frictions can be neglected. If a force P is applied at the mid-point of bar AB, in which case the bar can be in a equilibrium state?
A、
B、
C、
D、

2、A rigid body is in equilibrium state under the coplanar force system. Which set of equilibrium equations are not independent of each other?
A、SX = 0, Sx = 0, SmA(F) = 0
B、SmO(F) = 0, SmA(F) = 0, SmB(F) = 0
C、SmO(F) = 0, SmC(F) = 0, SY = 0
D、SX = 0, SY = 0, SmO(F) = 0

3、A rigid body is in equilibrium state under the coplanar force system. Which set of equilibrium equations are not independent of each other?
A、SX = 0, SmO(F) = 0, SmA(F) = 0
B、SmO(F) = 0, SmA(F) = 0, SmB(F) = 0
C、SmA(F) = 0, SmC(F) = 0, SY = 0
D、SX = 0, SmA(F) = 0, SmB(F) = 0

4、Consider the equilibrium of bar AB. The correct moment equation about point A should be
A、SmA(F) = m + Psinq × L/2 + M + mA = 0
B、SmA(F) = -m - Psinq × L/2 + M = 0
C、SmA(F) = -mL - P × L/2 + M + mA = 0
D、SmA(F) = -m - Psinq × L/2 + M + mA = 0

5、The whole system is in equilibrium state. Which set of equilibrium equations is correct?
A、Study ADB： ?mA(F) = NB×2L + YD×L = 0
B、Study the whole system： ?mA(F) = - P×(L+r) + NB×2L = 0
C、Study CDE and the pully： ?mD(F) = - P×r - T×(L – r) + XE×L + SBC×L×sin30° = 0
D、Study the whole system： ?mA(F) = - P×(L+r) + NB×2L - T×(L – r) = 0

6、A planar mechanism consists of three rigid bodies and is subjected to a force system in its plane. How many independent equilibrium equations can be created at most?
A、6
B、9
C、12
D、3

7、The whole system is in equilibrium state. Assume the member force in bar i (i=1,2,…5) is Si. Which set of equilibrium equations is correct?
A、Study AB： ?mA(F) = -q×L×L/2 + S2 ×L/2 - P×3L/4 = 0
B、Study ABCDE： ?mA(F) = -q×2L×L + S2 ×L/2 + S3×3L/2 - P×3L/4 + YB×L + NC×2L = 0
C、Study BC： ?mB(F) = -q×L×L/2 – S3 ×L/2 – S5×L/2 + NC×L = 0
D、Study ABCDE： ?mA(F) = -q×2L×L - P×3L/4 + NC×2L = 0

8、Consider the equilibrium of the whole system. Which sets of equilibrium equations are correct?
A、?mO(F) = - m - XA×L×sinj + YA×L×cosj - Q×2L×cosj - P× L×sinj + NB×3L×cosj = 0
B、?mO(F) = - m - Q×2L×cosj - P× L×sinj + NB×3L×cosj = 0
C、?mB(F) = - m - XA×2L×sinj - YA×2L×cosj + Q×L×cosj = 0
D、?mB(F) = - m - XO× L×sinj - YO×3L×cosj+ Q×L×cosj = 0

9、For a free-body diagram in one plane, which sets of equilibrium equations could be independent of each other?
A、three force equations
B、two force equations and one moment equation
C、one force equation and two moment equations
D、three moment equations

10、An action and its reaction have the same magnitude and are in opposite directions and collinear, so they form an equilibrium force system.

05 Composite motion of a point

Tests for week 3

1、The three bars O1A, O2B and AB are pin-connected in one plane. At the position shown, O1A//O2B. In which case bar AB undergoes translation when bars O1A and O2B rotate in the plane.
A、
B、
C、
D、

2、How many unknowns can be solved for based on the vector equation Va=Ve+Vr?
A、1
B、2
C、3
D、4

3、The motion path equation of a point is s = b + ct, where b and c are constant. Which statement is correct?
A、The motion path must be a straight line.
B、The motion path must be a curve.
C、The speed must be constant.
D、The acceleration must be zero.

4、Which statement is correct for a moving point?
A、If at is always equal to 0 and an is not equal to 0, then the point moves along a curve with varying speed.
B、If at is constant and an is not equal to 0, then the point moves along a curve with uniformly varying speed.
C、If at is not equal to 0 and an is always equal to 0, then the point moves along a curve with varying speed.
D、If at is not equal to 0 and an is always equal to 0, then the point moves along a straight line with constant speed.

5、A point moves along a curve with reducing speed. Which of the four drawings for the velocity and acceleration is possible?
A、
B、
C、
D、

6、A point moves along a circle with path coordinate s. The motion equation of the point can be expressed as . When the point moves to the highest point (M), the x and y coordinates of the acceleration should be
A、
B、
C、
D、

7、If a rigid body undergoes translation, then the motion path of a point on the rigid body
A、must be a straight line.
B、must be a planar curve.
C、cannot be a spatial curve.
D、could be a spatial curve.

8、The velocities of two arbitrary points A and B on a rigid body are vA and vB, respectively. Which statement is correct?
A、If the rigid body is in translation, then ?vA?=?vB? must be satisfied.
B、If ?vA?=?vB? is satisfied, then the rigid body must be in translation.
C、If the rigid body is in translation, then ?vA?=?vB? must be satisfied and the directions of the two velocities could be different.
D、If the rigid body is in translation, then the directions of vA and vB must be the same but probably |vA|1|vB|.

9、A right-angle bar is rotating around a fixed axis. The directions of the angular velocity ω and angular acceleration α are shown in the figures. Which one gives the correct directions for velocity, normal and tangential components of acceleration of point B?
A、
B、
C、
D、

10、If a rigid body is rotating around a fixed axis, then
A、at some instant, the accelerations of all points on a line perpendicular to the axis of rotation are not parallel to each other.
B、at some instant, the velocity magnitudes of any two points are proportional to their vertical distances to the axis of rotation.
C、at some instant, the velocities of any two points are parallel to each other.
D、it is impossible that the motion paths of all points are circular arcs.

11、In the mechanism, , , . Crank rotates with a constant angular velocity in clockwise direction. At the position shown, points , and are on one vertical line. Which equation is correct for the velocity/acceleration of point or ?
A、
B、
C、
D、

12、The disks are rotating around axes passing through point O. The accelerations of point M on the disks are shown. Which set of equations are correct?
A、
B、
C、
D、

13、The theorem of composition of velocities
A、is only valid when the transport motion is a translation.
B、is only valid when the transport motion is a rotation.
C、is not valid when the transport motion is a rotation.
D、is valid for any type of transport motion.

14、In the velocity parallelogram drawn based on the theorem of composition of velocities,
A、the absolute velocity is diagonal of the parallelogram formed by the transport velocity and relative velocity.
B、the transport velocity is diagonal of the parallelogram formed by the absolute velocity and relative velocity.
C、the relative velocity is diagonal of the parallelogram formed by the transport velocity and absolute velocity.
D、the algebraic sum of the projections of the absolute velocity, transport velocity and relative velocity on any axis is equal to zero.

15、In the mechanism, bar OA rotates with angular velocity w in counterclockwise direction. Which velocity parallelogram is correct if point B on bar BCD is chosen as the moving point and the moving reference frame is attached to bar OA?
A、
B、
C、
D、

16、In the mechanism, the disk rotates with angular velocity w in counterclockwise direction. Which velocity parallelogram is correct if point A on bar AB is chosen as the moving point and the moving reference frame is attached to the disk?
A、
B、
C、
D、

17、Crank OA rotates with angular velocity w and angular acceleration α. The accelerations are drawn in the figure if point A on crank OA is chosen as the moving point and the moving reference frame is attached to the T-shaped member. Which equation is correct according to the theorem of composition of accelerations?
A、
B、
C、
D、

18、In composite motion of a point, the transport velocity and acceleration at an instant are the velocity and acceleration of the point in the moving reference frame coinciding with the moving point.

06 Plane motion of rigid bodies

Tests for week 4

1、The planar motion of a rigid body can be resolved into a translation and a rotation. The angular velocity and angular acceleration with respect to base point are and , respectively. The angular velocity and angular acceleration with respect to base point are and , respectively. Which set of the following equations is correct?
A、
B、
C、.
D、

2、For the planar mechanism at the position shown, bar is in horizontal direction and bar is in vertical direction. At this instant, the velocity and acceleration of slider are and , respectively; the angular velocity and angular acceleration of bar are and , respectively; the angular velocity and angular acceleration of bar are and , respectively. Which set of the following equations is correct?
A、
B、
C、
D、

3、The relations of velocities of points and in the crank-connecting rod mechanism are shown. Which one could be correct?
A、
B、
C、
D、

4、Points and are any two arbitrary points in a plane figure. At a instant, the velocities of these two points are and , respectively; The accelerations of these two points are and , respectively. Which of the following equations is correct?
A、
B、
C、
D、

5、At a instant, the magnitudes of velocities of points and in a plane figure are and , respectively, and . Which drawings are impossible for the velocity directions?
A、
B、
C、
D、

6、Which are the correct methods to calculate the angular velocity of bar in the mechanism?
A、
B、
C、
D、

7、In the planar mechanism, the three bars (, and ), wheel and slider are pin-connected together. Bar rotates around point . Wheel rotates without slipping on the horizontal surface. Slider moves in vertical direction. Which statements are correct?
A、Point is the instantaneous center for velocities of wheel .
B、Point is the instantaneous center for velocities of bar .
C、Point is the instantaneous center for velocities of bar .
D、Point is the instantaneous center for velocities of bar .

8、In the planar mechanism, the small gear rotates without slipping on the big fixed gear . Crank rotates around point . Bar is pin-connected to gear and bar . Which statements are correct?
A、The contact point of the two gears is the instantaneous center for velocities of gear .
B、Point is the instantaneous center for velocities of gear .
C、Point is the instantaneous center for velocities of bar .
D、Point is the instantaneous center for velocities of bar .

9、A plane figure moves in its plane. The velocity vectors of two different points on the plane figure are the same at a instant. Which statements are correct?
A、All points in the plane figure have the same velocity at this instant.
B、All points in the plane figure have the same acceleration at this instant.
C、The angular acceleration of the plane figure must be zero, but the angular velocity may not be zero at this instant.
D、The angular velocity of the plane figure must be zero, but the angular acceleration may not be zero at this instant.

10、Points and are any two arbitrary points in a plane figure. The projections of the velocities of these two points on line are and , respectively. The projections of the accelerations of these two points on line are and , respectively. Then we can get and .

08 Principle of impulse and momentum

Test for week 5

1、A particle is subjected to forces of , , ? and , and the resultant of these forces is . Which statement is correct?
A、The moving direction of the particle must be the same as that of the resultant force .
B、The greater the resultant force , the greater the speed of the particle.
C、The greater the resultant force , the greater the acceleration of the particle.
D、The acceleration direction of the particle may or may not be the same as that of the resultant force .

2、A car passes through points , and on a road. The pressures on the road from the car are , and ，respectively, then
A、
B、
C、
D、

3、A sphere with weight is suspended by two cables and . Based on equilibrium analysis, the tensile force in the two cables should be . If cable is cut suddenly, the tensile force in cable will be at this instant. Which statement is correct?
A、
B、
C、
D、

4、For two particles with masses of and ，their speeds at some instant are and ，respectively. Which statement is correct?
A、If and ，the momenta of these two particles must be the same.
B、If and ，the momenta of these two particles can also be the same.
C、If and ，the momenta of these two particles can also be the same.
D、If and ，the momenta of these two particles must be different.

5、Three homogeneous disks , and have the same radius , the same weight and the same angular velocity . As shown, disk rotates around its mass center; disk rotates around a fixed axis on its edge; disk rotates without slipping on a horizontal surface. If the momenta of the three disks are , and , respectively, then
A、
B、
C、
D、

6、A homogeneous bar has a weight . One end of the bar contacts with the smooth ground and the other end is suspended by a cable. If the cable is cut at the position shown (), then
A、The motion path of the mass center will be a circular arc during the subsequent motion.
B、 when the bar falls to the ground.
C、 when the bar falls to the ground.
D、 when the bar falls to the ground.

7、Which statement is correct?
A、The momenta of a system of particles must be larger than the momentum of one particle in the system.
B、The momentum of each particle in a system is equal to zero, then the momenta of the whole system must be equal to zero.
C、The momentum of each particle in a system is not equal to zero, then the momenta of the whole system must not be equal to zero.
D、The magnitude of the momentum of a particle system must be equal to the summation of the magnitudes of the momenta of all particles in the system.

8、As shown, a cannonball with mass m is fired with initial velocity and emission angle . The air resistance is proportional to the cannonball velocity, i.e., , where is a constant. The differential equation of motion of the cannonball can be
A、
B、
C、
D、

9、A moving rigid body with mass has a momentum and mass center velocity , then should be satisfied.

10、A homogeneous disk rests on a smooth horizontal surface. If a couple formed by and is applied on the disk, there should be no displacement for the disk center.

10 Principle of work and kinetic energy

Test for week 6

1、A homogeneous disk with mass M and radius R is rotating around an axis passing through point O. The angular momentum of the disk about this axis should be
A、
B、
C、
D、

2、A homogeneous disk with mass M and radius R is rotating without slipping along an inclined plane. The velocity of the disk center is V. The angular momentum of the disk about the its contact point C with the plane should be
A、
B、
C、
D、

3、A slender bar with mass is composed of two homogeneous segments, which are made of steel and wood, respectively. The mass moment of inertia of bar about -, - and -axes are , and , respectively. Then we can get
A、
B、
C、
D、

4、The homogeneous pully has a mass and radius . Block A of mass and block of mass are suspended on the pully through a weightless cable. If the angular acceleration of the pully is in clockwise direction, then the differential equation of rotation of the pully should be
A、
B、
C、
D、

5、The two homogeneous rings in Figs. (a) and (d) and the two homogeneous disks in Figs. (b) and (c) have the same weight and radius . Force is applied in Figs. (a) and (b). A moment is applied in Fig. (c). A block with weight is suspended in Fig. (d). Which statement is correct?
A、The angular acceleration of the ring in Fig. (a) is equal to that of the disk in Fig. (b).
B、The angular acceleration of the ring in Fig. (a) is equal to that of the disk in Fig. (c).
C、The angular acceleration of the ring in Fig. (a) is equal to that of the ring in Fig. (d).
D、The angular acceleration of the disk in Fig. (b) is equal to that of the ring in Fig. (d).

6、A homogeneous disk C with weight P and radius r is rotating around point O with angular velocity w. The eccentricity is OC=e. The angular momentum of the disk about point O should be
A、
B、
C、
D、

7、The undeformed length of a spring is . One end of the spring is fixed and the other end is attached to a block. When the block moves from point to , from point to and from point to , the work done by the spring force is , and , respectively. Which of the following is correct?
A、
B、
C、
D、

8、A small sphere moves from point to point along a circular path in a vertical plane. If it moves along path , the work done by its gravity force is . If it moves along path , the work done by its gravity force is . Then we can get
A、
B、
C、
D、

9、A homogeneous bar has mass m and length . At the position shown, the angular velocity of the bar is . The velocities of points , and are , and ，respectively. Point is the instantaneous center for velocities of the bar. The kinetic energy of the bar at this instant should be
A、
B、
C、
D、

10、A small sphere with mass m moves from the same height to the ground along three different paths. It is assumed that the initial velocity is zero and all frictions can be neglected. If the velocities of the sphere when it reaches the ground are , and ，respectively, then
A、
B、
C、
D、

11、Two blocks and connected by a spring are put on a horizontal smooth surface. The spring is compressed and then released from rest suddenly. If the kinetic energy and momentum of the system are and , respectively, then
A、
B、
C、
D、

12、The three homogeneous rigid bodies (ring, disk and bar) have the same mass. They are all released from rest from the dash line positions, i.e., their mass centers and point are in a horizontal line. If the velocities of their mass centers are , and , respectively, when they move to the lowest position, then
A、
B、
C、
D、

13、As shown, -axis passes through the mass center of one body with mass m. - and - axes are parallel to -axis. The distances between - and - axes, - and - axes, and - and - axes are a, b and d, respectively. Based on the parallel-axis theorem for mass moment of inertia, we can get
A、
B、
C、
D、

14、A small sphere with mass m moves along a smooth semi-circular path . The initial velocity points downward. Which of the following statements are correct?
A、The momenta of the sphere are the same at point and point .
B、The momenta of the sphere are different at point and point .
C、The kinetic energy of the sphere is the same at point and point .
D、The kinetic energy of the sphere is different at point and point .

15、A small sphere with mass m moves along a smooth semi-circular path . The initial velocity points downward. Which of the following statements are correct?
A、The momentum is not conserved during the motion.
B、The angular momentum about point is conserved during the motion.
C、The angular momentum about point is not conserved during the motion.
D、The momentum is conserved during the motion.

16、The two wheels and have the same mass moment of inertia. A block with weight is suspended on wheel and a force is applied on wheel . . If the angular accelerations of the two wheels are and , respectively, then must be equal to .

17、The kinetic energy of a rigid body in plane motion can be determined by one-half of the product of its mass and the square of its velocity at the centroid.

18、The internal force of a particle system can change the kinetic energy of the particle system.

11 D'Alembert's principle

Test for week 7

1、A particle is subjected to its gravity force only. The inertial force is when the particle is in free falling motion. The inertial force is when the particle is thrown upright. We can have
A、
B、
C、
D、

2、Under a force applied at point , the trolley with weight is moving with acceleration a on a horizontal surface. Point is the mass center of the trolley. By D’Alembert’s Principle, the inertial force on the trolley should be
A、
B、
C、
D、

3、A homogeneous slender bar with length and mass rotates around point . At the position shown, bar has an angular velocity and angular acceleration . The inertial force system could be
A、
B、
C、
D、

4、A principal vector and principal moment can be obtained by reducing an inertial force system to one point (reduction center). Which statements are correct?
A、The principal vector depends on the position of the reduction center.
B、The principal moment depends on the position of the reduction center.
C、The principal vector doesn’t depend on the position of the reduction center.
D、The principal moment doesn’t depend on the position of the reduction center.

5、A homogeneous wheel with mass and radius rotates without slipping on a horizontal surface. Point is the instantaneous center for velocities of the wheel. The acceleration of the wheel center is . The inertial force system could be
A、
B、
C、
D、

6、A homogeneous wheel with mass and radius rotates without slipping on a horizontal surface. Point is the instantaneous center for velocities of the wheel. The acceleration of the wheel center is . The inertial force system could be
A、
B、
C、
D、

7、Two blocks with weights and are suspended on a homogeneous pulley with weight by a weightless cable. . A moment is applied on the pulley and the whole system is in a stationary state. The cable forces on blocks and are and , respectively. If the moment is removed suddenly, then must be larger than provided there is no relative sliding between the cable and the pulley.

8、Under a horizontal force , two blocks with masses and () are moving on a smooth surface. The two blocks in Fig. (a) are accelerating and the two blocks in Fig. (b) are decelerating. If the force exerted on block by block is , then must larger than .

13 Strain

Test for week 8

1、Based on the isotropy assumption, in all directions the material has the same
A、stress
B、deformation
C、displacement
D、mechanical properties

2、Which statement is correct?
A、The internal force on a cross section of a bar is the algebraic summation of the stresses on this cross section.
B、The stress on a cross section of a bar is the average internal force on this cross section.
C、Stress is the intensity of the internal force.
D、The internal force must be larger than the stress.

3、The relationship between internal force and stress is that
A、The internal force is smaller than the stress.
B、The internal force is the algebraic summation of the stress.
C、The internal force is a vector and the stress is a scalar.
D、The stress is the internal force per unit area.

4、The magnitude of the internal force of a bar depends on not only the external force but also the shape of its cross section.

5、The stress is the intensity of the internal force per unit area.

6、The volume element deforms from the solid line position to the dash line position. The shear strain must be .

15 Axial load

Test for week 9

1、The cross section area of a bar in tension is A. The normal stress on the inclined plane with inclined angle should be
A、
B、
C、
D、

2、The axial load on section n-n of the bar should be
A、-3P
B、-4P
C、4P
D、8P

3、For a bar under axial tension, the sections with the maximum normal stress and maximum shear stress are
A、the cross section and inclined section with inclined angle 45°, respectively.
B、both the cross sections.
C、the inclined section with inclined angle 45°and cross section, respectively.
D、both the inclined sections with inclined angle 45°.

4、Hooke’s law can be used for
A、ductile materials only.
B、axial tension only.
C、a case with the stress smaller than the proportional limit.
D、a case with the stress smaller than the yielding stress.

5、After strain hardening (cold hardening), the material shows
A、higher proportional limit and lower ductility.
B、higher proportional limit and ductility.
C、lower proportional limit and higher ductility.
D、lower proportional limit and ductility.

6、The maximum tensile force in the bar should be
A、12KN
B、20KN
C、8KN
D、13KN

7、The tensile rigidity of the bar with length 2l is EA. The total elongation of the bar should be
A、
B、
C、
D、

8、The bar is subjected to a force as shown. One end of the bar is fixed. Which statement is correct?
A、There is no deformation in segment AB.
B、There is no deformation in segment BC.
C、There is no displacement for any cross section in segment AB.
D、There is no displacement for any cross section in segment BC.

9、The bar with a slot in segment BC is subjected to tensile loading. Which of the following is correct for the axial forces and stresses in segment AB and BC?
A、
B、
C、
D、None of these is correct.

10、If the total elongation of a bar is zero, then there must be no displacement for each cross section of the bar.

11、Two bars made of two different materials have the same length and cross section area. If the axial loads in the two bars are the same, then the stresses on their cross sections must be also the same.

12、One wooden bar and one steel bar have the same cross section. If the external forces on these two bars are the same, then the internal forces in these two bars should be also the same.

17 Bending

Test for week 10

1、A hollow shaft is subjected to an external torque. Which of the following figures is correct for the shear stress distribution on the cross section of the shaft?
A、
B、
C、
D、

2、For the cantilever beam shown in the figure, the internal forces on section A should be
A、
B、
C、
D、

3、A distributed load is applied on a simply supported beam. Which statement is correct according to the relations among the distributed load intensity, the shearing force and the bending moment?
A、The shearing force diagram is a horizontal straight line and the bending moment diagram is a parabolic curve.
B、The shearing force diagram is a parabolic curve and the bending moment diagram is a horizontal straight line.
C、The shearing force diagram is a inclined straight line and the bending moment diagram is a parabolic curve.
D、The shearing force diagram is a parabolic curve and the bending moment diagram is a inclined straight line.

4、Which is correct for the internal forces at section C of the simply supported beam?
A、
B、
C、
D、

5、Which is correct for the signs of the internal torques in the shaft shown?
A、The internal torque is positive in segment AB and negative in segment BC.
B、The internal torque is negative in segment AB and positive in segment BC.
C、The internal torques in segments AB and BC are positive.
D、The internal torques in segments AB and BC are negative.

6、The factors affecting the magnitude of the angle of twist of a circular shaft include
A、the internal torque, material and length of the shaft.
B、the internal torque, length and torsional rigidity (GJ) of the shaft.
C、the internal torque, material and cross section geometry of the shaft.
D、the internal torque, length and cross section geometry of the shaft.

7、The inner and outer diameters of a hollow circular shaft are d and D, respectively. a=d/D. The polar moment of inertia of the shaft should be
A、
B、
C、
D、

8、A solid circular shaft is subjected to an external torque Mn. If the shaft is in linear elastic region, the shear stress distribution on its cross section should be
A、
B、
C、
D、

9、Two circular shafts with the same length are subjected to the same external torque. The diameter of the first shaft is one half of that of the second one. The ratio of the maximum shear stresses in these two shafts should be
A、2:1
B、4:1
C、8:1
D、16:1

10、A cantilever beam is subjected to a concentrated force. If the force is moved closer to the fixed end of the beam, then the maximum bending moment in the beam will
A、decrease.
B、keep constant.
C、increase.
D、decrease, increase or keep constant.

11、In section B of the cantilever beam shown,
A、there is a jump in the shear force diagram, and the bending moment diagram is continuous and smooth.
B、there is a sudden slope change in the shear force diagram and jump in the bending moment diagram.
C、there is a jump in both the shear force diagram and the bending moment diagram.
D、there is no jump in the shear force diagram, but there is a jump in the bending moment diagram.

12、The two beams have the same l, b and P. The cross sectional height of the first beam is two times of that of the second one. The maximum normal stress in the second beam will be ( ) of that of the first one.
A、2 times
B、4 times
C、6 times
D、8 times

13、A beam with rectangular cross section is subjected to pure bending. The normal stress distribution on the cross section should be
A、
B、
C、
D、

14、If a circular shaft is under torsion, then there should be only shear stresses and no normal stresses on its cross section.

15、If a circular shaft is under torsion, then all points having the same distance to the cross section center should have the same shear stress.

19 Combined loadings

Test for week 11

1、A steel bar is suspended by steel cables as shown. What type of deformation does segment AB of the bar undergo?
A、uniaxial compression
B、pure bending
C、combination of bending and tension
D、combination of bending and compression

2、The deformation of bar AD is
A、bending
B、compression
C、combination of bending and compression
D、combination of bending and tension

3、The deformation of bar AB is
A、bending
B、uniaxial tension/compression
C、combination of bending and compression
D、combination of bending and tension

4、A member made of cast iron is subjected to three forces as shown. Which point is the critical point?
A、point ①
B、point ②
C、point ③
D、point ④

5、Three bars are subjected to compression as shown. If the absolute values of the maximum compressive stresses in bars 1, 2 and 3 are σmax1, σmax2 and σmax3, respectively, then their relationship should be
A、σmax1<σmax2<σmax3
B、σmax1<σmax2=σmax3
C、σmax1<σmax3<σmax2
D、σmax1=σmax3<σmax3

6、The shaft is subjected to a concentrated force and an external torque. What’s the deformation of the shaft?
A、Segment AC is under torsion and segment CB is under bending.
B、Segment AC is under torsion and segment CB is under a combination of bending and torsion.
C、Segment AC is under a combination of bending and torsion and segment CB is under bending.
D、Both segments AC and CB are under a combination of bending and torsion.

7、There is no neutral layer (one layer without deformation) for a bar under the combination of tension and bending.

8、The deformation of a bar under eccentric compression is actually a combination of bending and compression.

21 Deflections of beams and shafts

Test for Week 12

1、The Mohr’s circle shown represents the stress state of an element under
A、uniaxial tension.
B、uniaxial compression.
C、pure shear.
D、biaxial tension.

2、For the element shown, its maximum shear stress should be
A、65MPa
B、60MPa
C、80MPa
D、50MPa

3、Which figure is correct for the shear stresses of an element? (unit: MPa)
A、
B、
C、
D、

4、For the element shown, its principal stresses should be
A、
B、
C、
D、

5、For the cantilever beam with length l, the deflection at the free end is . If the beam length is reduced to one half of its original length, then the deflection at the free end should be
A、
B、
C、
D、

6、On the principal plane of an element, we can get
A、the maximum normal stress
B、zero normal stress
C、the maximum shear stress
D、zero shear stress

7、Which figure is not correct for the stress states of the four points on the cantilever beam?
A、For point 1:
B、For point 2:
C、For point 3:
D、For point 4:

8、Which one is not correct if the coordinates of the center of a Mohr’s circle are represented by (σc,τc)?
A、σc＜0，τc＜0
B、σc＜0，τc＝0
C、σc＝0，τc＝0
D、σc＞0，τc＝0

9、Which condition cannot be used to calculate the integration constants when the integration method is used to determine the deflection curve equation?
A、
B、
C、
D、

10、In plane stress condition , the plane where the principal stresses locate is
A、the plane with extreme shear stress.
B、the plane with extreme shear and normal stresses.
C、the plane with extreme normal stress.
D、the plane without extreme shear and normal stresses.

11、The Mohr’s circle must be a point for an element under uniaxial stress state.

12、For a triaxial stress state, the Mohr’s circle must be a point if the three principal stresses are equal.

Final Exam

Final Exam for Engineering Mechanics

1、All weights and frictions can be neglected. If a force P is applied at the mid-point of bar AB, in which case the bar can be in a equilibrium state?
A、
B、
C、
D、

2、Consider the equilibrium of bar AB. The correct moment equation about point A should be
A、SmA(F) = m + Psinq × L/2 + M + mA = 0
B、SmA(F) = -m - Psinq × L/2 + M = 0
C、SmA(F) = -mL - P × L/2 + M + mA = 0
D、SmA(F) = -m - Psinq × L/2 + M + mA = 0

3、The whole system is in equilibrium state. Which set of equilibrium equations is correct?
A、Study ADB： ?mA(F) = NB×2L + YD×L = 0
B、Study the whole system： ?mA(F) = - P×(L+r) + NB×2L = 0
C、Study CDE and the pully： ?mD(F) = - P×r - T×(L – r) + XE×L + SBC×L×sin30° = 0
D、Study the whole system： ?mA(F) = - P×(L+r) + NB×2L - T×(L – r) = 0

4、The whole system is in equilibrium state. Assume the member force in bar i (i=1,2,…5) is Si. Which set of equilibrium equations is correct?
A、Study AB： ?mA(F) = -q×L×L/2 + S2 ×L/2 - P×3L/4 = 0
B、Study ABCDE： ?mA(F) = -q×2L×L + S2 ×L/2 + S3×3L/2 - P×3L/4 + YB×L + NC×2L = 0
C、Study BC： ?mB(F) = -q×L×L/2 – S3 ×L/2 – S5×L/2 + NC×L = 0
D、Study ABCDE： ?mA(F) = -q×2L×L - P×3L/4 + NC×2L = 0

5、The three bars O1A, O2B and AB are pin-connected in one plane. At the position shown, O1A//O2B. In which case bar AB undergoes translation when bars O1A and O2B rotate in the plane.
A、
B、
C、
D、

6、A point moves along a circle with path coordinate s. The motion equation of the point can be expressed as . When the point moves to the highest point (M), the x and y coordinates of the acceleration should be
A、
B、
C、
D、

7、A right-angle bar is rotating around a fixed axis. The directions of the angular velocity ω and angular acceleration α are shown in the figures. Which one gives the correct directions for velocity, normal and tangential components of acceleration of point B?
A、
B、
C、
D、

8、In the mechanism, , , . Crank rotates with a constant angular velocity in clockwise direction. At the position shown, points , and are on one vertical line. Which equation is correct for the velocity/acceleration of point or ?
A、
B、
C、
D、

9、In the mechanism, bar OA rotates with angular velocity w in counterclockwise direction. Which velocity parallelogram is correct if point B on bar BCD is chosen as the moving point and the moving reference frame is attached to bar OA?
A、
B、
C、
D、

10、In the mechanism, the disk rotates with angular velocity w in counterclockwise direction. Which velocity parallelogram is correct if point A on bar AB is chosen as the moving point and the moving reference frame is attached to the disk?
A、
B、
C、
D、

11、Crank OA rotates with angular velocity w and angular acceleration α. The accelerations are drawn in the figure if point A on crank OA is chosen as the moving point and the moving reference frame is attached to the T-shaped member. Which equation is correct according to the theorem of composition of accelerations?
A、
B、
C、
D、

12、A sphere with weight is suspended by two cables and . Based on equilibrium analysis, the tensile force in the two cables should be . If cable is cut suddenly, the tensile force in cable will be at this instant. Which statement is correct?
A、
B、
C、
D、

13、Three homogeneous disks , and have the same radius , the same weight and the same angular velocity . As shown, disk rotates around its mass center; disk rotates around a fixed axis on its edge; disk rotates with slipping on a horizontal surface. If the momenta of the three disks are , and , respectively, then
A、
B、
C、
D、

14、A homogeneous bar has a weight . One end of the bar contacts with the smooth ground and the other end is suspended by a cable. If the cable is cut at the position shown (), then
A、The motion path of the mass center will be a circular arc during the subsequent motion.
B、 when the bar falls to the ground.
C、 when the bar falls to the ground.
D、 when the bar falls to the ground.

15、The homogeneous pully has a mass and radius . Block A of mass and block of mass are suspended on the pully through a weightless cable. If the angular acceleration of the pully is in clockwise direction, then the differential equation of rotation of the pully should be
A、
B、
C、
D、

16、The undeformed length of a spring is . One end of the spring is fixed and the other end is attached to a block. When the block moves from point to , from point to and from point to , the work done by the spring force is , and , respectively. Which of the following is correct?
A、
B、
C、
D、

17、A homogeneous bar has mass m and length . At the position shown, the angular velocity of the bar is . The velocities of points , and are , and ，respectively. Point is the instantaneous center for velocities of the bar. The kinetic energy of the bar at this instant should be
A、
B、
C、
D、

18、The three homogeneous rigid bodies (ring, disk and bar) have the same mass. They are all released from rest from the dash line positions, i.e., their mass centers and point are in a horizontal line. If the velocities of their mass centers are , and , respectively, when they move to the lowest position, then
A、
B、
C、
D、

19、Under a force applied at point , the trolley with weight is moving with acceleration a on a horizontal surface. Point is the mass center of the trolley. By D’Alembert’s Principle, the inertial force on the trolley should be
A、
B、
C、
D、

20、A homogeneous slender bar with length and mass rotates around point . At the position shown, bar has an angular velocity and angular acceleration . The inertial force system could be
A、
B、
C、
D、

21、The axial load on section n-n of the bar should be
A、-3P
B、-4P
C、4P
D、8P

22、The maximum tensile force in the bar should be
A、12KN
B、20KN
C、8KN
D、13KN

23、The tensile rigidity of the bar with length 2l is EA. The total elongation of the bar should be
A、
B、
C、
D、

24、The bar with a slot in segment BC is subjected to tensile loading. Which of the following is correct for the axial forces and stresses in segment AB and BC?
A、
B、
C、
D、None of these is correct.

25、For the cantilever beam shown in the figure, the internal forces on section A should be
A、
B、
C、
D、

26、Which is correct for the internal forces at section C of the simply supported beam?
A、
B、
C、
D、

27、In section B of the cantilever beam shown,
A、there is a jump in the shear force diagram, and the bending moment diagram is continuous and smooth.
B、there is a sudden slope change in the shear force diagram and jump in the bending moment diagram.
C、there is a jump in both the shear force diagram and the bending moment diagram.
D、there is no jump in the shear force diagram, but there is a jump in the bending moment diagram.

28、The two beams have the same l, b and P. The cross sectional height of the first beam is two times of that of the second one. The maximum normal stress in the second beam will be ( ) of that of the first one.
A、2 times
B、4 times
C、6 times
D、8 times

29、A hollow shaft is subjected to an external torque. Which of the following figures is correct for the shear stress distribution on the cross section of the shaft?
A、
B、
C、
D、

30、A steel bar is suspended by steel cables as shown. What type of deformation does segment AB of the bar undergo?
A、uniaxial compression
B、pure bending
C、combination of bending and tension
D、combination of bending and compression

31、The deformation of bar AD is
A、bending
B、compression
C、combination of bending and compression
D、combination of bending and tension

32、A member made of cast iron is subjected to three forces as shown. Which point is the critical point?
A、point ①
B、point ②
C、point ③
D、point ④

33、Three bars are subjected to compression as shown. If the absolute values of the maximum compressive stresses in bars 1, 2 and 3 are σmax1, σmax2 and σmax3, respectively, then their relationship should be
A、σmax1<σmax2<σmax3
B、σmax1<σmax2=σmax3
C、σmax1<σmax3<σmax2
D、σmax1=σmax3<σmax3

34、The shaft is subjected to a concentrated force and an external torque. What’s the deformation of the shaft?
A、Segment AC is under torsion and segment CB is under bending.
B、Segment AC is under torsion and segment CB is under a combination of bending and torsion.
C、Segment AC is under a combination of bending and torsion and segment CB is under bending.
D、Both segments AC and CB are under a combination of bending and torsion.

35、The Mohr’s circle shown represents the stress state of an element under
A、uniaxial tension.
B、uniaxial compression.
C、pure shear.
D、biaxial tension.

36、For the element shown, its maximum shear stress should be
A、65MPa
B、60MPa
C、80MPa
D、50MPa

37、For the element shown, its principal stresses should be
A、
B、
C、
D、

38、For the cantilever beam with length l, the deflection at the free end is . If the beam length is reduced to one half of its original length, then the deflection at the free end should be
A、
B、
C、
D、

39、Which condition cannot be used to calculate the integration constants when the integration method is used to determine the deflection curve equation?
A、
B、
C、
D、

40、Consider the equilibrium of the whole system. Which sets of equilibrium equations are correct?
A、?mO(F) = - m - XA×L×sinj + YA×L×cosj - Q×2L×cosj - P× L×sinj + NB×3L×cosj = 0
B、?mO(F) = - m - Q×2L×cosj - P× L×sinj + NB×3L×cosj = 0
C、?mB(F) = - m - XA×2L×sinj - YA×2L×cosj + Q×L×cosj = 0
D、?mB(F) = - m - XO× L×sinj - YO×3L×cosj+ Q×L×cosj = 0

41、Points and are any two arbitrary points in a plane figure. At a instant, the velocities of these two points are and , respectively; The accelerations of these two points are and , respectively. Which of the following equations is correct?
A、
B、
C、
D、

42、At a instant, the magnitudes of velocities of points and in a plane figure are and , respectively, and . Which drawings are impossible for the velocity directions?
A、
B、
C、
D、

43、Which are the correct methods to calculate the angular velocity of bar in the mechanism?
A、
B、
C、
D、

44、In the planar mechanism, the three bars (, and ), wheel and slider are pin-connected together. Bar rotates around point . Wheel rotates without slipping on the horizontal surface. Slider moves in vertical direction. Which statements are correct?
A、Point is the instantaneous center for velocities of wheel .
B、Point is the instantaneous center for velocities of bar .
C、Point is the instantaneous center for velocities of bar .
D、Point is the instantaneous center for velocities of bar .

45、In the planar mechanism, the small gear rotates without slipping on the big fixed gear . Crank rotates around point . Bar is pin-connected to gear and bar . Which statements are correct?
A、The contact point of the two gears is the instantaneous center for velocities of gear .
B、Point is the instantaneous center for velocities of gear .
C、Point is the instantaneous center for velocities of bar .
D、Point is the instantaneous center for velocities of bar .

46、A homogeneous wheel with mass and radius rotates without slipping on a horizontal surface. Point is the instantaneous center for velocities of the wheel. The acceleration of the wheel center is . The inertial force system could be
A、
B、
C、
D、

学习通Engineering Mechanics

Engineering Mechanics（工程力学）是工程学科中的基础课程，它主要研究物体的运动和变形规律以及力的作用。对于工程学生而言，学习Engineering Mechanics是非常重要的，因为它是后续学习其他工程学科的基础。

课程内容

Engineering Mechanics包含三个主要分支：Statics（静力学）、Dynamics（动力学）和Mechanics of Materials（材料力学）。

Statics

Statics主要研究物体处于静止状态下的力的平衡问题。学习此分支需要掌握向量的概念、力的合成与分解、力的平衡条件等内容。

Dynamics

Dynamics主要研究物体在运动状态下的力学问题。学习此分支需要掌握牛顿运动定律、加速度的概念、运动学方程等内容。

Mechanics of Materials

Mechanics of Materials主要研究材料的变形与破坏问题。学习此分支需要掌握应力、应变、弹性模量等概念。

学习方法

学习Engineering Mechanics需要理论与实践相结合。以下是几个学习方法：

1. 理论学习：首先需要掌握相关的理论知识，包括公式、定理等。
2. 示例分析：通过分析一些典型的例子，更好地理解相关的知识点。
3. 练习题：大量的练习题可以帮助培养解决问题的能力。
4. 实验操作：通过实验操作，可以更好地理解相关的物理现象。

学习资源

学习Engineering Mechanics需要一些资源，以下是一些推荐：

1. 教材：可以选择一些经典的教材，如Russell C. Hibbeler的《Engineering Mechanics: Statics》。
2. 课程视频：可以在学习通等平台上找到相关的Engineering Mechanics课程视频。
3. 习题集：可以选择一些习题集进行练习。
4. 实验室：可以参加实验室课程，进行相应的实验操作。

结语

Engineering Mechanics是一门非常基础但又非常重要的工程学科，它为后续学习其他工程学科打下了坚实的基础。通过合理的学习方法和相关资源的利用，相信大家都能够掌握Engineering Mechanics的相关知识，为未来的工程学习打下坚实基础。

中国大学Engineering Mechanics

中国大学Engineering Mechanics是中国工程力学领域内的重要研究领域之一，目前已经成为了国际上学术界公认的重要学科之一。中国大学Engineering Mechanics是以研究力学、流体力学、固体力学、振动力学、复合材料力学等基础理论及其应用为主要研究方向的学科。

Engineering Mechanics作为一门学科，其所研究的内容极为广泛。其中，力学是最基础的一部分，主要研究物体在受到外力作用下的运动规律；流体力学则研究各种不同流体的流动规律；固体力学则主要研究物体的力学性质，例如弹性模量、材料的变形等；振动力学则研究物体在振动条件下的力学规律，包括自由振动、阻尼振动、强迫振动等；复合材料力学则主要研究各种不同复合材料的力学性质及其应用。

中国大学Engineering Mechanics是国内外工程力学领域内的重要学科之一，其研究成果在工程领域内有着广泛的应用。例如，工程力学的研究成果可以被应用于工程结构的设计、建筑物的抗震设计、航空航天领域的研究、交通运输领域的研究、海洋工程的研究等领域。

当前，中国大学Engineering Mechanics的研究方向正在不断扩展和深化。例如，中国大学Engineering Mechanics的研究方向正在向微观领域扩展，研究复合材料的基础理论及其应用；同时，中国大学Engineering Mechanics的研究方向也在向多学科交叉领域扩展，例如，与计算机科学、人工智能等学科进行深度融合，研究与工程力学相关的计算机算法、数据分析、人机交互等问题。

总的来说，中国大学Engineering Mechanics是一个充满活力、前景广阔、重要性不断提升的学科领域。未来，随着科技的发展和社会需求的变化，中国大学Engineering Mechanics的研究方向将会越来越广泛、越来越深入，其研究成果也将会为行业和社会带来更多的创新和进步。