WTC PHYS 2425 – Homework Solutions – Chapter 05 Prof. Doney
- In the figure below each of the suspended blocks has weight w. The pulleys are frictionless and the ropes have negligible weight. Calculate, in each case, the tension T in the rope in terms of the weight w. In each case, include the free-body diagram or diagrams you used to determine the answer.
case (a): (ANS: T = w)
case (b): (ANS: T = w)
case (c): (ANS: T = w)
- A large wrecking ball is held in place by two light steel cables. The mass m of the wrecking ball is 4099 kg, and θ = 37°.
(a) What is the tension in cable TB? (ANS: 50,300 N)
(b) What is the tension in cable TA? (ANS: 30,300 N)
- A1167-kg car is held in place by a light cable on a very smooth (frictionless) ramp, as shown in the figure below. The cable makes an angle of θ2 = 32.8° above the surface of the ramp, and the ramp itself rises at θ1 = 23.0° above the horizontal.
(a) Draw a free-body diagram for the car.
Key:(b) Find the tension in the cable. (ANS: 5320 N)
(c) How hard does the surface of the ramp push on the car? (ANS: 7650 N)
- A 130-kg (including all the contents) rocket has an engine that produces a constant vertical force (the thrust) of 1650 N. Inside this rocket, a 15.6-N electrical power supply rests on the floor.
(a) Find the acceleration of the rocket. (ANS: 2.89 m/s2)
(b) When it has reached an altitude of 120 m, how hard does the floor push on the power supply? (Hint: Start with a free-body diagram for the power supply.) (ANS: 20.2 N)
- Three sleds are being pulled horizontally on frictionless horizontal ice using horizontal ropes. The pull is horizontal and of magnitude 120 N. (Let m1 = 32.5 kg, m2 = 22.5 kg, and m3 = 10.5 kg.)
(a) Find the acceleration of the system. (ANS: 1.83 m/s2)
(b) Find the tension in ropes A and B. (ANS: TA = 101N, TB = 59.5 N)
- A 570 N physics student stands on a bathroom scale in an 850-kg (including the student) elevator that is supported by a cable. As the elevator starts moving, the scale reads 470 N.
- Find the acceleration of the elevator (magnitude and direction -- take up to be the positive direction).
(ANS: -1.72 m/s2)
(b) What is the acceleration if the scale reads 690 N? (ANS: 2.06 m/s2)
(c) If the scale reads zero, what is the acceleration of the elevator? (ANS: -9.8 m/s2)
Should the student worry? Explain your answer. (ANS: YES, b/c the elevator is in free fall)
(d) What is the tension in the cable in parts (a) and (c)? (ANS: (a) 6870N, (c) 0N)
- In a laboratory experiment on friction, a 441-N block resting on a rough horizontal table is pulled by a horizontal wire. The pull gradually increases until the block begins to move and continues to increase thereafter. The figure below shows a graph of the friction force on this block as a function of the pull.
(a) Identify the regions of the graph where static and kinetic friction occur.
(ANS: The friction is static for P = 0 to P = 75.0 N. The friction is kinetic for P > 75.0 N)
(b) Find the coefficients of static and kinetic friction between the block and the table. (ANS: us = 0.17, uk = 0.113)
(c) Why does the graph slant upward in the first part but then level out?
Key: When the block is moving the friction is kinetic and has the constant value fk = μkn, independent of P. This is why the graph is horizontal for P > 75.0 N. When the block is at rest, fs = P since this prevents relative motion. This is why the graph for P < 75.0 N has slope +1.
(d) What would the graph look like if a 441-N brick were placed on the block?
Key: Maximum fs and fk would double. The values of f on the vertical axis would double but the shape of the graph would be unchanged.
What would the coefficients of friction be in that case? (ANS: us = 0.17, uk = 0.113)
- If the coefficient of kinetic friction between tires and dry pavement is 0.77, what is the shortest distance in which you can stop an automobile by locking the brakes when traveling at 26.1 m/s (about 58 mi/h)? (ANS: 45.1m)
(b) On wet pavement the coefficient of kinetic friction may be only 0.24. How fast should you drive on wet pavement in order to be able to stop in the same distance as in part (a)? (Note: Locking the brakes is not the safest way to stop.) (ANS: 14.6 m/s)
- A flat (unbanked) curve on a highway has a radius of 280 m. A car rounds the curve at a speed of 28.0 m/s.
(a) What is the minimum coefficient of friction that will prevent sliding? (ANS: 0.286)
(b) Suppose the highway is icy and the coefficient of friction between the tires and pavement is only one-third what you find in part (a). What should be the maximum speed of the car so it can round the curve safely? (ANS: 16.2 m/s)
- Consider the system shown in the figure below. Block A weighs 41.0 N and block B weighs 20.8 N. Once block B is set into downward motion, it descends at a constant speed.
(a) Calculate the coefficient of kinetic friction between block A and the tabletop. (ANS: 0.507)
(b) A cat, also of weight 41.0 N, falls asleep on top of block A. If block B is now set into downward motion, what is its acceleration? (ANS: 1.98 m/s2 upward)
- The "Giant Swing" at a county fair consists of a vertical central shaft with a number of horizontal arms attached at its upper end. Each arm supports a seat suspended from a cable d1 = 5.10 m long, the upper end of the cable being fastened to the arm at a point d2 = 2.85 m from the central shaft.
(a) Find the time of one revolution of the swing if the cable supporting a seat makes an angle of θ = 29.0° with the vertical. (ANS: 6.22 s)
(b) Does the angle depend on the weight of the passenger for a given rate of revolution? (ANS: NO)
- In the figure below a worker lifts a weight w by pulling down on a rope with a force . The upper pulley is attached to the ceiling by a chain, and the lower pulley is attached to the weight by another chain.
In terms of w, find the tension in each chain and the magnitude of the force if the weight is lifted at constant speed. (ANS: T top chain = w, T bottom chain = 2, F = w/2)
Sketch the free-body diagram or diagrams you used to determine your answers. Assume that the rope, pulleys, and chains all have negligible weights.
Key: