Torque Homework
1.
After a skiing accident, your leg is in a cast and supported in a traction device, as shown in Figure 6-27. Find the magnitude of the force F exerted by the leg on the small pulley. (By Newton's third law, the small pulley exerts an equal and opposite force on the leg.) Let the mass m be 1.60 kg, and the angle θ be 26.0°.
1 N
Figure 6-27
2.
The gardening tool shown in Figure 11-24 is used to pull weeds. If a 1.04 N·m torque (about the pivot point) is required to pull a given weed, what force did the weed exert on the tool?
1 N
Figure 11-24
3.
A person holds a 1.42 N baseball in his hand, a distance of 2L = 33.9 cm from the elbow joint, as shown in Figure 11-26. The biceps, attached at a distance of d = 2.93 cm from the elbow, exert an upward force of 14.2 N on the forearm. Consider the forearm and hand to be a uniform rod with a mass of 1.17 kg.
Figure 11-26
(a) Calculate the magnitude of the net torque acting on the forearm and hand. Use the elbow joint as the axis of rotation.
1 N·m (b) If the net torque obtained in part (a) is nonzero, in which direction will the forearm and hand rotate?
2
counterclockwise no rotationclockwise
(c) Would the net torque exerted on the forearm and hand increase or decrease if the biceps were attached farther from the elbow joint? Explain.
3
4.
To determine the location of his center of mass, a physics student lies on a lightweight plank supported by two scales L = 4.90 m apart, as indicated in the figure below.
(a) If the left scale reads 292 N, and the right scale reads 135 N, find the student's mass.
1 kg
(b) Find the distance from the student's head to his center of mass.
2 m
5.
A school yard teeter totter with a total length of 5.7 m and a mass of 36 kg is pivoted at its center. A 16 kg child sits on one end of the teeter totter.
(a) Where should a parent push with a force of 218 N in order to hold the teeter totter level?
1 m (from the pivot)
(b) Where should the parent push with a force of 304 N to keep the teeter totter level?
2 m (from the pivot)
(c) How would your answers to parts (a) and (b) change if the mass of the teeter totter were doubled? Explain.
3
6.
An 85 kg person stands on a uniform 7.3 kg ladder that is 3.9 m long, as shown. The floor is rough; hence it exerts both a normal force, f1, and a frictional force, f2, on the ladder. The wall, on the other hand, is frictionless; it exerts only a normal force, f3. Using the dimensions in the figure, find the magnitudes of f1, f2, and f3.
f1 = / 1 Nf2 = / 2 N
f3 = / 3 N
7.
A cat walks along a uniform plank that is 4.00 m long and has a mass of 7.00 kg. The plank is supported by two sawhorses, one 0.44 m from the left end of the board and the other 1.63 m from its right end. When the cat nears the right end, the plank just begins to tip. If the cat has a mass of 4.9 kg, how close to the right end of the two-by-four can it walk before the board begins to tip?
1 m
8.
When you arrive at Duke's Dude Ranch, you are greeted by the large wooden sign shown in the figure below. The left end of the sign is held in place by a bolt, the right end is tied to a rope that makes an angle of θ = 22.3° with the horizontal.
(a) If the sign is uniform, 3.20 m long, and has a mass of 20.1 kg, what is the tension in the rope?
1 N
(b) What are the horizontal and vertical components of the force, F, exerted by the bolt?
2 N (horizontal)
3 N (vertical)
9.
A 4.94 m long diving board is supported by two pillars. One pillar is at the left end of the diving board, as shown below; the other is d = 1.55 m away. Find F1 and F2 as a function of the distance, x, of the swimmer from the left end of the diving board. (x = L in the figure below.) Assume that the diving board is uniform and has a mass of 82 kg and the diver has a mass of 89.5 kg. (Assume that g = 9.81.)
F1 = [(1 kN/m)x + 2 kN]
F2 = [(3 kN/m)x + 4 kN]