Deck 6: Torque and Equilibrium

Question 1

Figure 6.2 Force diagram with masses at each end of a pivoted bar of length (L+1) m.
A person of mass 70 kg stands 0.5 m from one end of a 2 m long uniform plank (of negligible mass) that is being held in equilibrium by two vertical ropes attached to the ends of the plank. What is the tension in the rope closer to the person?

A)23 N
B)47 N
C)229 N
D)457 N

Answer 1

457 N

Question 2

The drive chain on a bicycle applies a torque of 0.85 N m to the wheel of the bicycle. What force must be applied tangentially at the rim of the wheel, of diameter 0.7 m, to stop it accelerating?

A)1.21 N, radially along the wheel
B)1.21 N, tangentially to the wheel
C)2.43 N, radially along the wheel
D)2.43 N, tangentially to the wheel

Answer 2

2.43 N, tangentially to the wheel

Question 3

A cyclist goes around a curve of radius 10 m at a speed of 10 km/hr. At what angle to the horizontal must the cyclist lean to ensure that the net force of the ground on his body passes through his centre of gravity?

A)15°
B)20°
C)75°
D)85°

Answer 3

85°

Question 4

A truck is carrying a refrigerator that is 2.0 m tall and 0.8 m wide. The centre of mass of the refrigerator is at its geometric centre. It is facing sideways and a short strip on the bed of the truck keeps the refrigerator from sliding. What is the maximum acceleration that the truck can have before the refrigerator begins to tip over?

A)2.0 m/s²
B)3.9 m/s²
C)4.9 m/s²
D)9.8 m/s²

Question 5

Figure 6.1
In Fig. 6.1, two forces F₁ and F₂ act at the ends of a bar supported at its centre. The magnitude of F₂ is half that of F₁, and è = 45°. What is the value of angle for which the bar is in equilibrium?

A)16°
B)21°
C)30°
D)45°

Question 6

A 75 kg diver stands at the edge of a light 6 m diving board, which is supported by two pillars 2 m apart. Find the force exerted by the pillar further from the diver.

A)735 N downward
B)735 N upward
C)1470 N downward
D)1470 N upward

Question 7

A weigh scale measures the weight of an object by balancing its weight against that of a fixed "reference" weight sliding along a scale until equilibrium is reached. If the weight to be measured is suspended at twice its distance from the fulcrum, which of the following actions would NOT restore equilibrium?

A)quadrupling the reference weight
B)quadrupling the distance of the reference weight from the fulcrum
C)doubling the reference weight and its distance from the fulcrum
D)replacing the reference weight by two others of half its mass: one at the original position and the other 3 times further from the fulcrum

Question 8

A 75 kg diver stands at the edge of a light 6 m diving board that is supported by two pillars 2 m apart. What is the force exerted by the pillar nearer the diver?

A)735 N downward
B)735 N upward
C)1102 N upward
D)2205 N upward

Question 9

Figure 6.1
A uniform bar with a pivot (fulcrum) at its centre and oblique forces acting at each end is in equilibrium, as shown in Fig. 6.1. What is the condition for this equilibrium?

A)F₂sinè = F₁cos
B)F₁cosè = F₂cos
C)F₁sinè = F₂sin
D)F₁sinè = F₂cos

Question 10

A car drives over a weigh scale. When the two front wheels are on the scale, the weight measured is 6000 N. When the rear two wheels are on the scale, the weight measured is 7500 N. How far from the front wheels is the car's centre of mass if the wheels are 3.5 m apart?

A)0.7 m
B)1.56 m
C)1.94 m
D)2.8 m

Question 11

A 6.0 kg mass is held in the hand, with the upper arm vertical and the forearm bent 30° below the horizontal. The pivot is at the elbow, and the bicep muscle acts in a vertical line 5 cm in front of the pivot. The forearm is 40 cm long and has a mass of 2.5 kg, and may be assumed to have its centre of mass in the middle. How much force must a bicep muscle exert to maintain this configuration?

A)58 N
B)116 N
C)284.2 N
D)568.4 N

Question 12

A 1 kg mass and a 0.7 kg mass are attached to the two ends of a string that goes over a pulley with a radius of 0.1 m. Because of friction, the pulley does not begin to rotate. What is the magnitude of the frictional torque on the bearing of the pulley if the system is in static equilibrium?

A)0.03 N m
B)0.29 N m
C)0.58 N m
D)2.90 N m

Question 13

A man with upper body mass of 40 kg bends forward at the hip at an angle of 60° from the vertical, keeping his legs in a vertical position and his back straight. The effective pivot point is the pelvic cavity, located 6 cm from the line of the back muscles used to maintain this bending position. The centre of mass of the upper body is located 60 cm from the pelvic pivot. What is the force exerted by the back muscles?

A)40 N
B)200 N
C)392 N
D)1960 N

Question 14

How much force must a man of shoulder-height 1.8 m and mass 70 kg exert on both hands in order to do a push-up, assuming that his body's centre of mass is 1.0 m from his feet?

A)38.9 N
B)77.8 N
C)381.1 N
D)762.1 N

Question 15

Figure 6.2 Force diagram with masses at each end of a pivoted bar of length (L+1) m.
In Fig. 6.2, the normal force N is 20 N and masses m_A and m_B, where m_B = 2m_A, hang in equilibrium at the ends of a uniform bar of mass m_bar = m_A/2 and length (L+1) m, exerting loads w_A and w_B, respectively. What are the values of m_bar and L that give equilibrium?

A)0.29 kg, 2/7 m
B)0.29 kg, 5/7 m
C)2.86 kg, 2/7 m
D)2.86 kg, 5/7 m

Question 16

A 20 kg child is sitting on a teeter-totter, 2 m from the pivot. What force is required when applied 0.7 m from the pivot in order to lift the child?

A)29 N
B)57 N
C)280 N
D)560 N

Question 17

A car travels around a corner at high speed. Why is it more likely to roll when there is a weight strapped to the roof?

A)There is more area for a side-wind to exert force.
B)The centrifugal force causes a sideways force on the car.
C)The centrifugal force is larger than the weight of the car.
D)The centre of gravity is higher off the ground, causing the centrifugal force to exert larger torque on the car.

Question 18

A woman is holding a 5.0 kg suitcase at arm's length, a distance of 0.4 m from her shoulder. What is the torque on the shoulder joint if her arm is horizontal?

A)1.0 N m
B)2.0 N m
C)19.6 N m
D)196.0 N m

Question 19

A refrigerator 2.0 m tall and 0.8 m wide has its centre of mass at its geometric centre. You are attempting to slide it along the floor by pushing horizontally on the side of the refrigerator. The coefficient of static friction between the floor and the refrigerator is 0.4. Depending on where you push, the refrigerator may start to tip over before it starts to slide along the floor. What is the highest distance above the floor that you can push the refrigerator so that it won't tip before it begins to slide?

A)0.4 m
B)1.0 m
C)1.2 m
D)2.0 m

Question 20

A man is holding a 5.0 kg suitcase at arm's length, a distance of 0.4 m from his shoulder. What is the torque on the shoulder joint if his arm is 30° below the horizontal?

A)0.9 N
B)1.7 N
C)17.0 N
D)34.0 N

Question 21

A skater is spinning with her arms high and near the axis of rotation. If she stretched her arms to horizontal position, which of the following outcomes would happen to her angular momentum and her speed?

A)Angular momentum would increase and speed would decrease.
B)Angular momentum would stay the same and speed would decrease.
C)Angular momentum would stay the same and speed would increase.
D)Angular momentum would decrease and speed would decrease.

Question 22

A hockey player swings his stick to hit a stationary puck. Describe the torques exerted on the player by this action.

Question 23

If a uniform rectangular box resting on the ground is pushed, depending on the height at which it is pushed, it may either slide or tip.

Question 24

Suppose you stir a cup of coffee, then place it at rest on an almost frictionless surface, such as ice. Describe the subsequent motion of the cup of coffee.

Question 25

If net torque on the body is constant, angular momentum is conserved.

Question 26

All forces acting on a body contribute to the torque on the body.

Question 27

When two (circular) curling rocks collide, they will not begin to rotate if they collide head-on.

Question 28

When a weight is being lifted using a hand, the force exerted by the muscle in the forearm is less than the weight being lifted.

Question 29

When two uniform spherical balls of equal mass but different diameters undergo a head-on collision, the rotation speeds of the balls change.

Question 30

A fly revolves at the edge of a turntable. How would angular momentum and speed change if it landed half way to the centre of a turntable?

A)Angular momentum would double and speed would double.
B)Angular momentum would stay the same and speed would reduce to 1/2.
C)Angular momentum would stay the same and speed would double.
D)Angular momentum would decrease and speed would reduce to 1/2.

Question 31

A uniform thickness, equilateral triangular plate is placed on a pivot passing through the centre of the area of the triangle. The triangle is in equilibrium.

Question 32

The brakes on a car are applied by brake shoes pressing down radially onto a circular brake drum. Describe the motion of the car as the pressure on the brake shoes increases with time.

Question 33

If a spinning skater pulled his arms toward his body, the angular momentum would remain the same.

Question 34

If the net force on an object is zero, the net torque on the object must also be zero.

Question 35

For equilibrium of an extended body, the vector sum of all forces must be zero.

Question 36

What is the necessary condition for conservation of angular momentum?

A)Net torque exerted on the body is zero.
B)Net torque exerted on the body is constant.
C)Angular acceleration of the rotating body is constant.
D)No forces are acting on the body.

Question 37

If the torque on a body is zero, then the vector sum of all forces is zero.

Question 38

Figure 6.3 Concurrent forces and non-concurrent forces. (a) The lines of action of concurrent forces pass through a common point. (b) The lines of action of non-concurrent forces do not intersect at a common point.
Explain why it is safer to lift a heavy weight by first bringing it closer to your feet before lifting.

Question 39

Figure 6.3 Concurrent forces and non-concurrent forces. (a) The lines of action of concurrent forces pass through a common point. (b) The lines of action of non-concurrent forces do not intersect at a common point.
Three forces are acting on objects as shown in Fig. 6.3. The vector sum of the forces is zero. Explain if there is any difference between the two cases: (a) the lines of action of concurrent forces pass through a common point, and (b) the lines of action of non-concurrent forces do not intersect at a common point. Are any of the two objects moving? Why or why not? If there were motion, what kind of motion would it be?

Question 40

The magnitude of the torque exerted by a force of magnitude F is equal to the perpendicular distance from the axis of rotation r⊥ multiplied by F. This is equivalent to saying it is equal to the distance from the axis of rotation r multiplied by the magnitude of the perpendicular component of the force, F⊥.

Question 41

Figure 6-4 ​
A 200 g hamster is running along a horizontal wheel, 26 cm in diameter, at 30 cm/s, remaining in the same spot with respect to the table. Suddenly, it slips and spins for a while with the wheel at the same speed. What is the hamster's angular momentum with respect to the centre of the wheel (a) while it is running and (b) while it spins with the wheel?

Question 42

Explain why placing the heaviest items in a bookcase on the lowest shelf makes it more stable against tipping over than if the heaviest books were on higher shelves.

Question 43

Explain why, when resting a ladder against a wall, it should not be at a large angle from the vertical.

Question 44

A uniform bar has different masses attached at each end, and rests on ice. It is pushed in the middle at right angles to its length. Assuming no friction with the ice, describe the subsequent motion of this object.

Question 45

Explain why, when a car turns a corner, the car dips down on the outside of the curve.

Question 46

If a uniform rectangular box resting on the ground is pushed, depending on the height at which it is pushed it may either slide or tip. Discuss what conditions determine whether sliding or tipping occurs.

Question 47

Figure 6-4 ​
A ball of mass 1 kg is flying horizontally and hits the hand with velocity 1.5 m/s, producing rotation of the underarm around the joint. The place where the ball hits the hand is at a distance l = 0.4 m from the joint (see Fig. 6.4). The underarm and hand together have a mass of 1.77 kg. What is the speed of the arm and the ball after the catch, assuming that no muscles were fighting the rotation?

Question 48

Why must the two pillars supporting a diving board not be too close together?