Chapter 8

A pile driver falls a distance of \(2.50 \mathrm{~m}\) before hitting a pile. Find its velocity as it hits the pile.

Given: $$ \begin{aligned} m &=11.4 \mathrm{~kg} \\ g &=9.80 \mathrm{~m} / \mathrm{s}^{2} \\ h &=22.0 \mathrm{~m} \\ E_{p} &=? \end{aligned} $$

Given: $$ \begin{aligned} W &=132 \mathrm{~J} \\ t &=7.00 \mathrm{~s} \\ P &=? \end{aligned} $$

Given:$$ \begin{aligned} F &=10.0 \mathrm{~N} \\ s &=3.43 \mathrm{~m} \\ W &=? \end{aligned} $$

Given: $$ \begin{aligned} m &=3.50 \mathrm{~kg} \\ g &=9.80 \mathrm{~m} / \mathrm{s}^{2} \\ h &=15.0 \mathrm{~m} \\ E_{p} &=? \end{aligned} $$

A pump is capable of developing \(4.00 \mathrm{~kW}\) of power. How many litres of water per minute can be lifted a distance of \(35.0 \mathrm{~m} ?(1 \mathrm{~L}\) of water has a mass of \(1 \mathrm{~kg} .\) )

A piece of shattered glass falls from the 8 2nd floor of a building, \(27 \overline{0} \mathrm{~m}\) above the ground. What is the velocity of the glass when it hits the ground, if air resistance is disregarded?

Given: $$ \begin{aligned} m &=4.70 \mathrm{~kg} \\ v &=9.60 \mathrm{~m} / \mathrm{s} \\ E_{k} &=? \end{aligned} $$

Given: $$ \begin{gathered} P=75.0 \mathrm{~W} \\ W=40.0 \mathrm{~J} \\ t=? \end{gathered} $$

Given: $$ \begin{aligned} F &=1850 \mathrm{~N} \\ s &=625 \mathrm{~m} \\ \theta &=37.5^{\circ} \\ W &=? \end{aligned} $$

A \(10.0\) -kg mass is dropped from a hot air balloon at a height of \(325 \mathrm{~m}\) above the ground. Find its speed at points \(30 \overline{0} \mathrm{~m}, 20 \overline{0} \mathrm{~m}\), and \(10 \overline{0} \mathrm{~m}\) above the ground and as it hits the ground.

Given: $$ \begin{aligned} E_{p} &=93.6 \mathrm{~J} \\ g &=9.80 \mathrm{~m} / \mathrm{s}^{2} \\ m &=2.30 \mathrm{~kg} \\ h &=? \end{aligned} $$

Given: $$ \begin{aligned} W &=55.0 \mathrm{~J} \\ t &=11.0 \mathrm{~s} \\ P &=? \end{aligned} $$

A truck with mass \(95 \overline{0}\) slugs is driven \(55.0 \mathrm{mi} / \mathrm{h}\). (a) What is its velocity in \(\mathrm{ft} / \mathrm{s}\) ? (b) What is its kinetic energy?

The work required to lift a crate is \(31 \overline{0} \mathrm{~J}\). If the crate is lifted in \(25.0 \mathrm{~s}\), what power is developed?

A bullet with mass \(12.0 \mathrm{~g}\) travels \(415 \mathrm{~m} / \mathrm{s}\). Find its kinetic energy. (Hint: Convert \(12.0 \mathrm{~g}\) to \(\mathrm{kg}\).)

When a \(36 \overline{0} 0\) -lb automobile runs out of gas, it is pushed by its unhappy driver and a friend a quarter of a mile \((0.250 \mathrm{mi})\). To keep the car rolling, they must exert a constant force of \(175 \mathrm{lb}\). (a) How much work do they do? (b) If it takes them \(15.0\) min, how much power do they develop? (c) Expressed in horsepower, how much power do they develop?

Given: $$ \begin{aligned} F &=m a \\ m &=16.0 \mathrm{~kg} \\ a &=9.80 \mathrm{~m} / \mathrm{s}^{2} \\ s &=13.0 \mathrm{~m} \\ W &=? \end{aligned} $$

A sandbag is dropped from a hot air balloon at a height of \(125 \mathrm{~m}\) above the ground. Find its velocity as it hits the ground. Disregard air resistance.

A bicycle and rider together have a mass of \(7.40\) slugs. If the kinetic energy is \(742 \mathrm{ft} \mathrm{lb}\), find the velocity.

An electric golf cart develops \(1.25 \mathrm{~kW}\) of power while moving at a constant speed. (a) Express its power in horsepower. (b) If the cart travels \(20 \overline{0} \mathrm{~m}\) in \(35.0 \mathrm{~s}\), what force is exerted by the cart?

How much work is required for a mechanical hoist to lift a \(9000-\mathrm{N}\) automobile to a height of \(1.80 \mathrm{~m}\) for repairs?

An ironworker drops a hammer \(5.25 \mathrm{~m}\) to the ground. What is its speed as it hits the ground?

A crate of mass \(475 \mathrm{~kg}\) is raised to a height \(17.0 \mathrm{~m}\) above the floor. What potential energy has it acquired with respect to the floor?

A hay wagon is used to move bales from the field to the barn. The tractor pulling the wagon exerts a constant force of \(350 \mathrm{lb}\). The distance from field to barn is \(\frac{1}{2}\) mi. How much work (ft \(l\) b) is done in moving one load of hay to the barn?

A box is dropped \(3.60 \mathrm{~m}\) to the ground. What is its speed as it hits the ground?

How long would it take a \(95 \overline{0}-\mathrm{W}\) motor to raise a \(36 \overline{0}-\mathrm{kg}\) mass to a height of \(16.0 \mathrm{~m} ?\)

A worker lifts 75 concrete blocks a distance of \(1.50 \mathrm{~m}\) to the bed of a truck. Each block has a mass of \(4.00 \mathrm{~kg} .\) How much work is done to lift all the blocks to the truck bed?

A piece of broken glass with mass \(15.0 \mathrm{~kg}\) falls from the side of a building \(8.00 \mathrm{~m}\) above the street. (a) What is the kinetic energy of the glass as it hits the street? (b) What is the speed of the glass as it hits the street?

The potential energy of a girder, after being lifted to the top of a building, is \(5.17 \times 10^{5} \mathrm{ftlb}\). If its mass is 173 slugs, how high is the girder?

A 1500 -lb casting is raised \(22.0\) ft in \(2.50\) min. Find the required horsepower.

The work required to lift eleven \(94.0\) -lb bags of cement from the ground to the back of a truck is \(4340 \mathrm{ft} \mathrm{lb}\). What is the distance from the ground to the bed of the truck?

A ball is thrown downward from the top of a building at a speed of \(75 \mathrm{ft} / \mathrm{s}\). Find its velocity as it hits the ground \(475 \mathrm{ft}\) below. Disregard air resistance.

A \(30.0\) -g bullet is fired from a gun and possesses \(1750 \mathrm{~J}\) of kinetic energy. Find its velocity.

What is the rating in \(\mathrm{kW}\) of a \(2.00\) -hp motor?

The Hoover Dam is \(726 \mathrm{ft}\) high. Find the potential energy of \(1.00\) million \(\mathrm{ft}^{3}\) of water at the top of the dam. (1 \(\mathrm{ft}^{3}\) of water weighs \(62.4 \mathrm{lb}\).)

A wattmeter shows that a motor is drawing \(2200 \mathrm{~W}\). What horsepower is being delivered?

How much work is done lifting a \(20 \overline{0}-\mathrm{kg}\) wrecking ball \(6.50 \mathrm{~m}\) above the ground?

A 250 -kg part falls from a plane and hits the ground at \(150 \mathrm{~km} / \mathrm{h}\). Find its kinetic energy.

A \(525-\mathrm{kg}\) steel beam is raised \(30.0 \mathrm{~m}\) in \(25.0 \mathrm{~s}\). How many kilowatts of power are needed?

A gardener pushes a mower a distance of \(90 \overline{0} \mathrm{~m}\) in mowing a yard. The handle of the mower makes an angle of \(40.0^{\circ}\) with the ground. The gardener exerts a force of \(35.0 \mathrm{~N}\) along the handle of the mower (Fig. 8.8). How much work does the gardener do in mowing the lawn?

A \(2.00-\mathrm{kg}\) projectile is fired vertically upward with an initial velocity of \(98.0 \mathrm{~m} / \mathrm{s}\). Find its kinetic energy, its potential energy, and the sum of its kinetic and potential energies at each of the following times: (a) the instant of its being fired (b) \(t=1.00 \mathrm{~s}\) (c) \(t=2.00 \mathrm{~s}\) (d) \(t=5.00 \mathrm{~s}\) (e) \(t=10.00 \mathrm{~s}\) (f) \(t=12.00 \mathrm{~s}\) (g) \(t=15.00 \mathrm{~s}\) (h) \(t=20.00 \mathrm{~s}\)

A meteorite is a solid composed of stone and/or metal material from outer space that passes through the atmosphere and hits the earth's surface. Find the kinetic energy of a meteorite with mass \(250 \mathrm{~kg}\) that hits the earth at \(25 \mathrm{~km} / \mathrm{s}\).

How long would it take a \(4.50-\mathrm{kW}\) motor to raise a \(175-\mathrm{kg}\) boiler to a platform \(15.0 \mathrm{~m}\) above the floor?

A traveler is pulling a suitcase at an angle of \(40.0^{\circ}\) with the horizontal (Fig. 8.9). If she exerts a force of \(5.00 \mathrm{lb}\) along the handle, how much work does the traveler do in pulling the suitcase \(\frac{1}{4} \mathrm{mi}\) ?

Water is pumped at \(25 \overline{0} \mathrm{~m}^{3} / \mathrm{min}\) from a lake into a tank \(65.0 \mathrm{~m}\) above the lake. (a) What power, in \(\mathrm{kW}\), must be delivered by the pump? (b) What horsepower rating does this pump motor have? (c) What is the increase in potential energy of the water each minute?

A \(475-\mathrm{kg}\) pre-stressed concrete beam is to be raised \(10.0 \mathrm{~m}\) in \(24.0 \mathrm{~s} .\) How many kilowatts of power are needed for the job?

A crate is pulled \(675 \mathrm{ft}\) across a warehouse floor by a worker using a rope that makes an angle of \(50.0^{\circ}\) with the floor. If \(375 \mathrm{lb}\) is exerted on the rope, how much work is done in pulling the crate across the floor?

Oil is pumped at \(25.0 \mathrm{~m}^{3} / \mathrm{min}\) into a tank \(10.0 \mathrm{~m}\) above the ground (1 \(\mathrm{L}\) of oil has a mass of \(0.68 \mathrm{~kg}\) ). (a) What power, in \(\mathrm{kW}\), must be delivered by the pump? (b) What is the increase in potential energy of the oil after \(10.0 \mathrm{~min} ?\) (c) Find the increase in potential energy of the oil after \(10.0 \mathrm{~min}\) if the tank is \(5.00 \mathrm{~m}\) above the ground.

A \(50.0-\mathrm{kg}\) welder is to be raised \(15.0 \mathrm{~m}\) in \(12.0 \mathrm{~s}\). How many kilowatts of power are needed for the job?