A 60-kg housepainter stands on a 15-kg aluminum platform. The platform is attached to a rope that passes through an overhead pulley, which allows the painter to raise herself and the platform (Figure 4-57).

$(b)$ When her speed reaches $1.0 \mathrm{~m} / \mathrm{s}$, she pulls in such a way that she and the platform go up at a constant speed. What force is she exerting on the rope now? (Ignore the mass of the rope.)

You need to raise a heavy block by pulling it with a massless rope. You can either (a) pull the block straight up height $h$, or (b) pull it up a long, frictionless plane inclined at a $15^{\circ}$ angle until its height has increased by $h$. Assume you will move the block at constant speed either way. Will you do more work in case a or case b? Or is the work the same in both cases? Explain.

Motive power for the experimental 10-Mg bus comes from the energy stored in a rotating flywheel which it carries. The flywheel has a mass of 1500 kg and a radius of gyration of 500 mm and is brought up to a maximum speed of 4000 rev/min. If the bus starts from rest and acquires a speed of 72 km/h at the top of a hill 20 m above the starting position, compute the reduced speed N of the flywheel. Assume that 10 percent of the energy taken from the flywheel is lost. Neglect the rotational energy of the wheels of the bus. The 10-Mg mass includes the flywheel.

A $1.5\ \mathrm{kg}$ object moves up the y-axis at a constant speed . When it reaches the origin, the forces $F_1 = 5.0\ \mathrm{N}$ at $37^\circ$ above the +x -axis, $F_2 = 2.5\ \mathrm{N}$ in the +x -direction , $F_3 = 3.5\ \mathrm{N}$ at $45^\circ$ below the - x-axis, and $F_4 = 1.5\ \mathrm{N}$ in the -y -direction are applied to it. (a) Will the object continue to move along the y-axis? (b) If not, what simultaneously applied force will keep it moving along the y-axis at a constant speed?

A roller-coaster car at an amusement park has a mass of 1200 kg when fully loaded with passengers. As the car passes over the top of a circular hill of radius 18 m, assume that its speed is not changing. At the top of the hill, what are the (a) magnitude

$$F_N$$

and (b) direction (up or down) of the normal force on the car from the track if the car’s speed is ν = 11 m/s? What are (c)

$$F_N$$

and (d) the direction if ν = 14 m/s?

A resort uses a rope to pull a 55-kg skier up a $40 ^ { \circ }$ slope at constant speed for 100 m. (a) Calculate the tension in the rope if the coefficient of kinetic friction between snow and skis is $\mu _ { k } = 0.20$. (b) How much work does the rope do on the skier?

Some flying fish travel in the air up to a quarter of a mile by using a lift force F to overcome their weight W while in the air. The lift force is modeled by

$$F ( v ) = 0.24 v ^ { 2 } , \text { where } v \geq 0$$

is the initial air speed in meters per second. A flying fish swimming with a current leaps out of the water with a speed that is 5 units greater than normal. Write a function G (v) for the lift force. What transformation does this represent?

An object is projected with initial speed $v_{0}$ from the edge of the roof of a building that has height H. The initial velocity of the object makes an angle $\alpha_{0}$ with the horizontal. Neglect air resistance. If $\alpha_{0}$ is 90$^{\circ}$, so that the object is thrown straight up (but misses the roof on the way down), what is the speed v of the object just before it strikes the ground?

You sling a shovelful of dirt up from the bottom of a hole with an initial velocity of 32 ft/sec. The dirt must rise 17 ft above the release point to clear the edge of the hole. Is that enough speed to get the dirt out, or had you better duck?

A carpenter on the roof of a building accidentally drops her hammer. As the hammer falls it passes two windows of equal height, as shown in Figure 2-32. Choose the best explanation from among the following:

I. The greater speed at window 2 results in a greater increase in speed.

II. Constant acceleration means the hammer speeds up the same amount for each window.

III. The hammer spends more time dropping past window 1.

You lean out of your dorm window, which is 12 m above the ground, and toss a 0.12-kg ball up to a friend at a window 11 m above you. (a) What is the slowest initial speed at which you can throw the ball so that he just catches it? (b) If you throw the ball at this speed and your friend misses it, what is its kinetic energy the instant before it hits the ground? (c) Suppose you throw the ball directly downward at the speed calculated in part a. What is its kinetic energy just before it hits the ground?

A 71 kg baseball player jumps straight up to catch a hard-hit ball. If the 140 g ball is moving horizontally at 28 m/s, and the catch is made when the ballplayer is at the highest point of his leap, what is his speed immediately after stopping the ball?

A block slides up a frictionless, inclined plane with $\theta=25^{\circ}$ (shown in the given figure).

(a) If the block reaches a maximum height $h=4.5 \mathrm{~m}$, what was the initial speed of the block?

(b) Now consider a second inclined plane with the same tilt angle and for which the coefficient of kinetic friction between the block and the plane is $\mu_K=0.15$. What initial speed is now required for the block to reach the same maximum height?

An ocean buoy moves up and down once every $4 \mathrm{~s}$ because of passing water waves. What is the wavelength of the waves if their speed is $3 \mathrm{~m} / \mathrm{s}$?
A. $0.75 \mathrm{~m}$
B. $133 \mathrm{~m}$
C. $7 \mathrm{~m}$
D. $12 \mathrm{~m}$