Deck 8: Equilibrium and Elasticity

Question 1

A uniform 200 kg beam,6 m long,is freely pivoted at P.The beam is supported in a horizontal position by a light strut,5 m long,which is freely pivoted at Q and is loosely pinned to the beam at R.A load of mass is suspended from the end of the beam at S.A maximum compression of 25,000 N in the strut is permitted,due to safety.In the figure,the maximum mass M of the load is closest to:

A)920 kg
B)665 kg
C)1175 kg
D)1120 kg
E)1375 kg

Answer 1

920 kg

Question 2

A small branch is wedged under a rock and rests on a smaller object.The smaller object is 2.0 m from the large rock and the branch is 10.0 m long.If the mass of the branch is 20.0 kg what force must be exerted on the smaller rock?

A)490 N
B)200 N
C)49 N
D)50 N

Answer 2

490 N

Question 3

In the figure,what mass M is required to balance the mobile?

A)18 g
B)30 g
C)36 g
D)60 g
E)90 g

Answer 3

36 g

Question 4

A steel wire,3.2 m long,has a diameter of 1.2 mm.The wire stretches 1.6 mm when it bears a load.Young's modulus for steel is 2.0 x 1011 n/m².The mass of the load is closest to:

A)12 kg
B)16 kg
C)20 kg
D)24 kg
E)28 kg

Question 5

In the figure,the Achilles tendon exerts a force F = 720 N.What is the torque it exerts about the ankle joint?

A)12.2 N ∙ m
B)16.2 N ∙ m
C)21.2 N ∙ m
D)25.9 N ∙ m
E)36.0 N ∙ m

Question 6

A 100 kg nonuniform boom,6.0 m long,is loosely pinned at the pivot at P.A 700 kg block is suspended from the end of the boom at A.The boom forms a 30° angle with the horizontal,and is supported by a cable,4.0 m long,between points D and B.Point B is 4.0 m from P,and point D is 4.0 m above P.The center of mass of the boom is at point C,which is 2.0 m from P.In the figure,the y-component of the pivot force on the boom at P is closest to:

A)2500 N
B)4200 N
C)6100 N
D)7800 N
E)8100 N

Question 7

An irregularly shaped object 10 m long is placed with each end on a scale.If the scale on the right reads 74 N and the scale on the left reads 93 N,how far from the left is the center of gravity?

A)4.4 m
B)13 m
C)5.6 m
D)8.0 m

Question 8

A 50 kg uniform ladder,5.0 m long,is placed against a smooth wall at a height of h = 3.7 m.The base of the ladder rests on a rough horizontal surface whose coefficient of static friction is 0.40.An 80 kg block is suspended from the top rung of the ladder,just at the wall.In the figure,the magnitude of the force exerted on the base of the ladder,due to contact with the rough horizontal surface is closest to:

A)1580
B)1560
C)1550
D)1600
E)1610

Question 9

A 20 kg uniform door has a width of 1.2 m and a height of 2.5 m. The door is mounted on a post by a pair of hinges, marked 1 and 2, at the top and bottom of the door. An external force of 60 N, at an angle of 30° above the horizontal, is applied to the doorknob, as shown. The doorknob is 1.0 m above the bottom of the door.
In the figure,the x-component of the force,exerted on the door at the bottom by hinge 2,is closest to:

A)zero
B)+29 N
C)+65 N
D)-29 N
E)-65 N

Question 10

A uniform 600 kg beam,6 m long,is freely pivoted at P.The beam is supported in a horizontal position by a light strut,5 m long,which is freely pivoted at Q and is loosely pinned to the beam at R.A load of mass is suspended from the end of the beam at S.A maximum compression of 25,000 N in the strut is permitted,due to safety.In the figure,under maximum load the y-component of the force exerted on the beam by the pivot at P is closest to:

A)7060 N
B)4560 N
C)9560 N
D)10,000 N
E)zero

Question 11

A uniform sign is supported at P as shown in the figure.If the sign is a square 0.7 m on its side and its mass is 7.0 kg,what is the magnitude of the horizontal force that P experiences?

A)34 N
B)0 N
C)24 N
D)98 N

Question 12

In the figure,a ladder of weight 200 N and length 10 meters leans against a smooth wall (no friction on wall).A firefighter of weight 600 N climbs a distance x up the ladder.The coefficient of friction between the ladder and the floor is 0.5.What is the maximum value of x if the ladder is not to slip?

A)3.93 m
B)5.00 m
C)6.04 m
D)6.28 m
E)8.44 m

Question 13

A 20 kg uniform door has a width of 1.2 m and a height of 2.5 m. The door is mounted on a post by a pair of hinges, marked 1 and 2, at the top and bottom of the door. An external force of 60 N, at an angle of 30° above the horizontal, is applied to the doorknob, as shown. The doorknob is 1.0 m above the bottom of the door.
In the figure,the x-component of the force,exerted on the door at the top by hinge 1,is closest to:

A)zero
B)+55 N
C)+80 N
D)-55 N
E)-80 N

Question 14

A winch is being used to raise a 100 N load.If the motor supplies a torque at a radius of 1.4 m and the cylinder upon which the rope is being wrapped has a radius a 0.6 m,how much force must the motor supply to keep the load suspended in place while the work crew goes to lunch?

A)43 N
B)230 N
C)80 N
D)70 N

Question 15

A uniform 600 kg beam,6 m long,is freely pivoted at P.The beam is supported in a horizontal position by a light strut,5 m long,which is freely pivoted at Q and is loosely pinned to the beam at R.A load of mass is suspended from the end of the beam at S.A maximum compression of 18,000 N in the strut is permitted,due to safety.In the figure,under maximum load,the x-component of the force exerted on the beam by the pivot at P is closest to:

A)10,800 N
B)14,400 N
C)12,600 N
D)16,200 N
E)18,000 N

Question 16

A uniform 1200 N beam that is 3.50 m long is suspended horizontally by two vertical wires at its ends.A small but dense 550 N weight is placed on the beam 2.00 m from one end,as shown in the figure.The tensions,A and B,in the two wires are:

A)A = 875 N,B = 875 N
B)A = 836 N,B = 914 N
C)A = 8960 N,B = 8190 N
D)A = 914 N,B = 836 N
E)A = 8190 N,B = 8960 N

Question 17

A 100 kg nonuniform boom,6.0 m long,is loosely pinned at the pivot at P.A 600 kg block is suspended from the end of the boom at A.The boom forms a 30° angle with the horizontal,and is supported by a cable,4.0 m long,between points D and B.Point B is 4.0 m from P,and point D is 4.0 m above P.The center of mass of the boom is at point C,which is 2.0 m from P.In the figure,the tension in the cable is closest to:

A)9300 N
B)8400 N
C)8100 N
D)7500 N
E)6900 N

Question 18

A 20 kg uniform door has a width of 1.2 m and a height of 2.5 m. The door is mounted on a post by a pair of hinges, marked 1 and 2, at the top and bottom of the door. An external force of 60 N, at an angle of 30° above the horizontal, is applied to the doorknob, as shown. The doorknob is 1.0 m above the bottom of the door.
In the figure,the sum of the y-components of the forces,exerted on the door by hinges 1 and 2,is closest to:

A)145 N
B)165 N
C)195 N
D)225 N
E)250 N

Question 19

A 40 kg uniform ladder,5.0 m long,is placed against a smooth wall at a height of h = 4.0 m.The base of the ladder rests on a rough horizontal surface whose coefficient of static friction is 0.40.An 80 kg block is suspended from the top rung of the ladder,just at the wall.In the figure,the force exerted on the wall by the ladder is closest to:

A)740 N
B)1300 N
C)980 N
D)900 N
E)1100 N

Question 20

A 500 kg nonuniform boom,6.0 m long,is loosely pinned at the pivot at P.A 800 kg block is suspended from the end of the boom at A.The boom forms a 30° angle with the horizontal,and is supported by a cable,4.0 m long,between points D and B.Point B is 4.0 m from P,and point D is 4.0 m above P.The center of mass of the boom is at point C,which is 2.0 m from P.In the figure,the X-component of the pivot force on the boom at P is closest to:

A)12,000 N
B)5500 N
C)19,000 N
D)7100 N
E)3200 N

Question 21

A car is being towed at constant velocity on a horizontal road using a horizontal chain.The tension in the chain must be equal to the weight of the car in order to maintain constant velocity.

Question 22

Which of the following is an accurate statement?

A)The ratio stress/strain is called the elastic modulus.
B)"Strain" has a meaning very close to "force."
C)"Stress" has a meaning very close to "stretch."
D)Tensile stress is measured in Newtons.
E)Tensile strain is measured in meters.

Question 23

A box of mass m is pulled with a constant acceleration a along a horizontal frictionless floor by a wire that makes an angle of 15 degrees above the horizontal.The tension in this wire is greater than ma.

Question 24

A stone rolls down a sloping hillside.The normal force that the surface of the hill exerts on the stone is equal to the stone's weight.

Question 25

Two unequal weights are connected by a massless string which passes over a frictionless pulley.If the pulley has no appreciable mass,the tension in the string is the same on both sides of the pulley;but if the pulley has mass,the tension will not be the same on both sides of the pulley.

Question 26

Two blocks,A and B,are being pulled to the right along a horizontal surface by a horizontal 100 N pull,as shown in the figure.Both of them are moving together at a constant velocity of 2.0 m/s to the right,and both weigh the same.Which of the figures below shows a correct free-body diagram of the horizontal forces acting on lower block,B?

A)

B)

C)

D)

E)None of these diagrams is correct.

Question 27

A man pushes against a rigid,immovable wall.Which of the following is the most accurate statement concerning this situation?

A)The man can never exert a force on the wall that exceeds his weight.
B)If the man pushes on the wall with a force of 200 N,we can be sure that the wall is pushing back with a force of exactly 200 N on him.
C)Since the wall cannot move,it cannot exert any force on the man.
D)The man cannot be in equilibrium since he is exerting a net force on the wall.
E)The friction force on the man's feet is directed to the left.

Question 28

An object attached to a spring is pulled across a frictionless surface.If the spring constant is 45 N/m and the spring is stretched by 0.88 m when the object is accelerating at 1.4 m/s2,what is the mass of the object?

A)28 kg
B)24 kg
C)31 kg
D)36 kg

Question 29

A force of 30 N stretches a spring 0.73 m from equilibrium.What is the value of the spring constant?

A)41 N/m
B)22 N/m
C)34 N/m
D)46 N/m

Question 30

If two forces of equal magnitude act on an object that is hinged at a pivot,the force acting farther from the pivot must produce the greater torque about the pivot.

Question 31

Three forces A, B, and C act on a body as shown. A fourth force F is required to keep the body in equilibrium.
In the figure,the x-component of force F is closest to:

A)+19 N
B)+28 N
C)+32 N
D)-28 N
E)-32 N

Question 32

Suppose that a heavy person and a light person are balanced on a teeter-totter made of a plank of wood.Each person now moves in toward the fulcrum a distance of 25 cm.What effect will this have on the balance of the teeter-totter?

A)The teeter-totter will remain in balance.
B)The heavy person's end will go down.
C)The light person's end will go down.
D)One cannot tell whether either end will rise or fall without knowing the relative mass of the plank.
E)Only if the plank has significant mass will the light person's end go down.

Question 33

Three forces A, B, and C act on a body as shown. A fourth force F is required to keep the body in equilibrium.
In the figure,the y-component of force F is closest to:

A)+24 N
B)+28 N
C)+32 N
D)-28 N
E)-32 N

Question 34

A spring stretches by 21.0 cm when a 135 N object is attached.What is the weight of a fish that would stretch the spring by 44.9 cm?

A)289 N
B)63 N
C)176 N
D)405 N

Question 35

If the forces on an object balance,it does not necessarily follow that the torques balance.

Question 36

Do all points on a rigid,rotating body have the same angular acceleration? Support your answer.

Question 37

In the figure,a block of mass M hangs in equilibrium.The rope that is fastened to the wall is horizontal and has a tension of 38 N.The rope that is fastened to the ceiling has a tension of 59 N and makes an angle Θ with the ceiling.The angle Θ is:

A)50°
B)40°
C)33°
D)65°
E)45°

Question 38

The figure shows two forces acting on an object.They have magnitudes F₁ = 9.6 N and F₂ = 3.2 N.What third force will cause the object to be in equilibrium?

A)10 N at 162° counterclockwise from
B)10 N at 108° counterclockwise from
C)6.4 N at 162° counterclockwise from
D)6.4 N at 108° counterclockwise from

Question 39

In the figure,a certain type of string will break if the tension in the string exceeds 300 N.A number of 8-kg weights are hung one below the other from a hook in the ceiling using this string.The number of weights that causes the string to break and the string segment that will break are as follows:

A)When the 4th weight is added,the top string segment will break.
B)Each segment has a tension of 78.4000015 N,and there is no limit to the number of weights that can be suspended.
C)When the 4th weight is added,the bottom string segment will break.
D)When the 4th weight is added,all string segments will break.
E)When the 38th weight is added,all string segments will break.