Physics Homework #6

1. A bead with mass 2.0 × 10-2 kg is moving along a wire in the positive direction of an x axis. Beginning at time t = 0, when the bead passes through x = 0 with speed 12 m/s, a constant force acts on the bead. The figure indicates the bead’s position at times t0 = 0, t1 = 1.0 s, t2 = 2.0 s, and t3 = 3.0 s. The bead momentarily stops at t = 3.0 s. What is the kinetic energy of the bead at t = 10 s?

2. A floating ice block is pushed through a displacement along a straight embankment by rushing water, which exerts a force on the block. How much work does the force do on the block during the displacement?
6205 Units: J

3. In the figure, a horizontal force of magnitude 18.0 N is applied to a 3.05 kg book as the book slides a distance d = 0.67 m up a frictionless ramp at angle θ = 30°. (a) During the displacement, what is the net work done on the book by , the gravitational force on the book, and the normal force on the book? (b) If the book has zero kinetic energy at the start of the displacement, what is its speed at the end of the displacement?

4. During spring semester at MIT, residents of the parallel buildings of the East Campus dorms battle one another with large catapults that are made with surgical hose mounted on a window frame. A balloon filled with dyed water is placed in a pouch attached to the hose, which is then stretched through the width of the room. Assume that the stretching of the hose obeys Hooke’s law with a spring constant of 130 N/m. If the hose is stretched by 4.70 m and then released, how much work does the force from the hose do on the balloon in the pouch by the time the hose reaches its relaxed length?

1435.85 Units: J

5. The force on a particle is directed along an x axis and given by F = F0(x/x0 – 1) where x is in meters and F is in Newtons. If F0 = 1.2 N and x0 = 2.7 m, find the work done by the force in moving the particle from x = 0 to x = 2×0 m.
0 Units: J

6. The figure gives the acceleration of a 4.0 kg particle as an applied force moves it from rest along an x axis from x = 0 to x = 9.0 m. The scale of the figure’s vertical axis is set by as = 10.0 m/s2. How much work has the force done on the particle when the particle reaches (a) x = 4.0 m, (b) x = 7.0 m, and (c) x = 9.0 m? What is the particle’s speed and direction (give positive answer if the particle moves along x axis in positive direction and negative otherwise) of travel when it reaches (d) x = 4.0 m, (e) x = 7.0 m, and (f) x = 9.0 m?

7. The loaded cab of an elevator has a mass of 1.5 × 103 kg and moves 239 m up the shaft in 16 s at constant speed. At what average rate does the force from the cable do work on the cab?
219580 Units: W
8. (a) At a certain instant, a particle-like object is acted on by a force while the object’s velocity is . What is the instantaneous rate at which the force does work on the object? (b) At some other time, the velocity consists of only a y component. If the force is unchanged, and the instantaneous power is -16 W, what is the velocity of the object just then? (Give your answer without a unit vector.)
a. 45.77 Units: W
8.42 Units: m/s

9. An initially stationary 2.8 kg object accelerates horizontally and uniformly to a speed of 8.7 m/s in 3.8 s. (a) In that 3.8 s interval, how much work is done on the object by the force accelerating it? What is the instantaneous power due to that force (b) at the end of the interval and (c) at the end of the first half of the interval?

10. To push a 27.0 kg crate up a frictionless incline, angled at 25.0° to the horizontal, a worker exerts a force of 219 N parallel to the incline. As the crate slides 1.9 m, how much work is done on the crate by (a) the worker’s applied force, (b) the gravitational force on the crate, and (c) the normal force exerted by the incline on the crate? (d) What is the total work done on the crate?