Boxes are transported from one location to another in a warehouse by means of a conveyor belt that moves with a constant speed of 0.50 m/s. At a certain location the conveyor belt moves for 2.0 m up an incline that makes an angle of 10° with the horizontal, then for 2.0 m horizontally, and finally for 2.0 m down an incline that makes an angle of 10° with the horizontal. Assume that a 2.0 kg box rides on the belt without slipping. At what rate is the force of the conveyor belt doing work on the box as the box moves (a) up the 10° incline, (b) horizontally, and (c) down the 10° incline?

A monkey has a cart with a horizontal spring attached to it that she uses for different tricks.In one trick, the monkey sits on the vibrating cart. When the cart reaches its maximum displacement from equilibrium, the monkey picks up a $0.30-\mathrm{kg}$ cantaloupe from a trainer. The mass of the monkey and the cart together is $3.0 \mathrm{kg}$. The spring constant is $660 \mathrm{N} / \mathrm{m}$.The amplitude of horizontal vibrations is $0.24 \mathrm{m}$.Determine the ratio of the maximum speed of the monkey before and after she picks up the cantaloupe.

A gardener pushes a $12 \mathrm{~kg}$ lawnmower whose handle is tilted up $37^{\circ}$ above horizontal. The lawnmower's coefficient of rolling friction is $0.15$. How much power does the gardener have to supply to push the lawnmower at a constant speed of $1.2 \mathrm{~m} / \mathrm{s}$ ? Assume his push is parallel to the handle.

An amusement park ride consists of a car moving in a vertical circle on the end of a rigid boom of negligible mass. The combined weight of the car and riders is 5.0 kN, and the radius of the circle is 10 m. At the top of the circle, what is the direction (up or down) of the force $F_B$ on the car from the boom if the car's speed is $v=$ $5.0 \mathrm{~m} / \mathrm{s}$ ?

The $160-\mathrm{Mg}$ train starts from rest and begins to climb the slope $\tan\theta = 1/10$. If the engine exerts a traction force $\mathbf{F}$ of $1 / 8$ of the weight of the train, determine the speed of the train when it has traveled up the slope a distance of $1 \mathrm{~km}$. Neglect rolling resistance.

Many speculative plans for spaceships capable of interstellar travel have been developed over the years. Nearly all are powered by the fusion of light nuclei, one of the very few power sources capable of providing the incredibly large energies required. A typical design for a fusion-powered craft has a $1.7 \times 10^6 \mathrm{~kg}$ ship brought up to a speed of $0.12 c$ using the energy from the fusion of ${ }_1^2 \mathrm{H}$ and ${ }_2^3 \mathrm{He}$. Each fusion reaction produces a daughter nucleus and one free proton with a combined kinetic energy of $18 \mathrm{MeV}$; these high-speed particles are directed backward to create thrust.
a. What is the kinetic energy of the ship at the noted top speed? For the purposes of this problem, you can do a nonrelativistic calculation.
b. If we assume that $50 \%$ of the energy of the fusion reactions goes into the kinetic energy of the ship (a very generous assumption), how many fusion reactions are required to get the ship up to speed?
c. How many kilograms of ${ }_1^2 \mathrm{H}$ and of ${ }_2^3 \mathrm{He}$ are required to produce the required number of reactions?

Three up quarks and one down quark make up a proton.

A 2.0 kg steel sphere is hanging from a hook by a thin wire $1 \mathrm{~m}$ long. You wish to strike it horizontally with a $0.5 \mathrm{~kg}$ hammer hard enough for the sphere to swing up $45^{\circ}$. Assuming that the hammer makes an elastic collision with the sphere, with what speed must you hit the sphere?

An object projected vertically upward passes every height less than the maximum twice, once on the way up and once on the way down. Show that the speed is the same in each direction. Measure height in feet. (take g as 32 feet per second per second or as 9.8 meters per second per second.)

A child on a sled slides down an icy slope, starting at a speed of 2.5 m/s. The slope makes a $15 ^ { \circ }$ angle with the horizontal. After sliding 10 m down the slope, the child enters a flat, slushy region, in which she slides for 2.0 s with a constant negative acceleration of $- 1.5 \mathrm { m } / \mathrm { s } ^ { 2 }$ with respect to her direction of motion. She then slides up another icy slope that makes a $20 ^ { \circ }$ angle with the horizontal. How far up the second slope does she slide?

The automobile path shown in Figure 3-31 is made up of straight lines and arcs of circles. The automobile starts from rest at point A. After it reaches point B, it travels at constant speed until it reaches point E. It comes to rest at point F.

$(c)$ How do the magnitudes of the acceleration compare for segments BC and DE?

A man is running around a circular track that is $200 \mathrm{~m}$ in circumference. An observer uses a stopwatch to record the runner's time at the end of each lap, obtaining the data in the following table.

(a) What was the man's average speed (rate) between $68 \mathrm{~s}$ and $152 \mathrm{~s}$ ?

(b) What was the man's average speed between $263 \mathrm{~s}$ and $412 \mathrm{~s}$ ?

(c) Calculate the man's speed for each lap. Is he slowing down, speeding up, or neither?

The motor used on a conveyor belt is 85% efficient. If the overall efficiency is 75%, what is the efficiency of the conveyor belt assembly?

Modify Example $3.19$ so that the arm starts from rest and spins up to its final rotation speed. The moment of inertia of the arm about $O$ is $I_0$. Neglecting air drag, find $d \omega / d t$ and integrate to find the angular velocity $\omega(t)$, assuming $\omega=0$ at $t=0$.