Chapter 5 | Energy

What is the kinetic energy of a 0.135-kg baseball thrown at 40.0 m/s (90.0 mph)?

108 J

SI unit of KE

Joule

Equation of Kinetic Energy

KE = 1/2mv^2

A hill is 100 m long and makes an angle of 12 with the horizontal. As a 50-kg jogger runs up the hill, how much work does gravity do on the jogger?

-10 000 J

A 2.00-kg ball has zero potential and kinetic energy. Maria drops the ball into a 10.0-m-deep well. After the ball comes to a stop in the mud, the sum of its potential and kinetic energy is:

-196 J.

A 50.0-kg (including the passenger) sled is subject to a net force of 20.0 N pushing in the direction of the sled's motion as it is moving over a horizontal surface for a distance of 11.0 m after having started from rest. At this point the sled is released as it starts down a 10.0° incline. However, the snow is not very deep, and the sled stops after having moved an additional 35.0 m. What is the work done by friction while the sled is on the incline?

-3200 J

A horizontal force of 200 N is applied to a 55-kg cart across a 10-m level surface. If the cart accelerates at 2.0 m/s2, then what is the work done by the force of friction as it acts to retard the motion of the cart?

-900 J

A 2.00-kg ball has zero kinetic and potential energy. Ernie drops the ball into a 10.0-m-deep well. Just before the ball hits the bottom, the sum of its kinetic and potential energy is:

0

A very light cart holding a 300-N box is moved at constant velocity across a 15-m level surface. What is the net work done in the process?

0

A satellite is held in orbit by a 2 000-N gravitational force. Each time the satellite completes an orbit of circumference 80 000 km, the work done on it by gravity is:

0 J

I use a rope 2.00 m long to swing a 10.0-kg weight around my head. The tension in the rope is 20.0 N. In half a revolution how much work is done by the rope on the weight?

0 J

I drop a 60-g golf ball from 2.0 m high. It rebounds to 1.5 m. How much energy is lost?

0.29 J

An automobile delivers 30.0 hp to its wheels when moving at a constant speed of 22.0 m/s. What is the resistance force on the automobile at this speed? (1 hp = 746 watts)

1 020 N

A force of 100 N is applied to a 50-kg mass in the direction of motion for a distance of 6.0 m and then the force is increased to 150 N for the next 4.0 m. For the 10 m of travel, how much work is done by the varying force?

1 200 J

Hooke's law spring is mounted horizontally over a frictionless surface. The spring is then compressed a distance d and is used to launch a mass m along the frictionless surface. What compression of the spring would result in the mass attaining double the kinetic energy received in the above situation?

1.41 d

A simple pendulum, 1.00 m in length, is released from rest when the support string is at an angle of 35.0 degree from the vertical. What is the speed of the suspended mass at the bottom of the swing? (g = 9.80 m/s2 and ignore air resistance)

1.88 m/s

A Hooke's law spring is compressed 12.0 cm from equilibrium and the potential energy stored is 72.0 J. What is the spring constant in this case?

10 000 N/m

An 80 000-kg airliner is flying at 900 km/h at a height of 10.0 km. What is its total energy (kinetic + potential) if the total was 0 when the airliner was at rest on the ground?

10 300 MJ

A pole vaulter clears 6.00 m. With what speed does he strike the mat in the landing area?

10.8 m/s

A 15.0-kg crate, initially at rest, slides down a ramp 2.0 m long and inclined at an angle of 20 degree with the horizontal. If there is no friction between ramp surface and crate, what is the kinetic energy of the crate at the bottom of the ramp? (g = 9.8 m/s2)

100 J

A girl and her bicycle have a total mass of 40 kg. At the top of the hill her speed is 5.0 m/s. The hill is 10 m high and 100 m long. If the force of friction as she rides down the hill is 20 N, what is her speed at the bottom?

11 m/s

A rock is thrown straight up with an initial velocity of 15.0 m/s. Ignore energy lost to air friction. How high will the rock rise?

11.5 m

Adisa pulls a 40-N crate up a 5.0-m long inclined plane at a constant velocity. If the plane is inclined at an angle of 37 to the horizontal and there is a constant force of friction of 10 N between the crate and the surface, what is the net change in potential energy of the crate?

120 J

Rupel pushes a box 5.00 m by applying a 25.0-N horizontal force. What work does she do?

125 J

A 7.00-kg bowling ball falls from a 2.00-m shelf. Just before hitting the floor, what will be its kinetic energy? (g = 9.80 m/s2 and assume air resistance is negligible)

137 J

An amount of work equal to 1.5 J is required to compress the spring in a spring-gun. What is the "launch speed" of a 15-g marble?

14 m/s

A Hooke's law spring is compressed 12.0 cm from equilibrium, and the potential energy stored is 72.0 J. What compression (as measured from equilibrium) would result in 100 J being stored in this case?

14.1 cm

A 200-hp engine can deliver, in SI units, an average power of ____. (1 hp = 746 W)

149 000 W

The net force acting on a 12.6-kg object is given by Fx = (20 x) N, where Fx is in newtons and x is in meters. How much work is done on the object as it moves from x = 0 to x = 10 m?

150 J

A baseball catcher puts on an exhibition by catching a 0.150-kg ball dropped from a helicopter at a height of 100 m above the catcher. If the catcher "gives" with the ball for a distance of 0.750 m while catching it, what average force is exerted on the mitt by the ball? (g = 9.80 m/s2)

197 N

A girl and her bicycle have a total mass of 40.0 kg. At the top of the hill her speed is 5.0 m/s, and her speed doubles as she rides down the hill. The hill is 10.0 m high and 100 m long. How much kinetic energy and potential energy is lost to friction?

2 420 J

A Hooke's law spring is mounted horizontally over a frictionless surface. The spring is then compressed a distance d and is used to launch a mass m along the frictionless surface. What compression of the spring would result in the mass attaining double the speed received in the above situation?

2.00 d

A simple pendulum, 2.0 m in length, is released with a push when the support string is at an angle of 25 degree from the vertical. If the initial speed of the suspended mass is 1.2 m/s when at the release point, what is its speed at the bottom of the swing? (g = 9.8 m/s2)

2.3 m/s

Yuri, a Russian weightlifter, is able to lift 250 kg 2.00 m in 2.00 s. What is his power output?

2.45 kW

Samantha pushes a 50-N crate up a ramp 25.0 m in length and inclined at 10 with the horizontal. What potential energy change does the crate experience?

220 J

A jet engine develops 1.0 105 N of thrust in moving an airplane forward at a speed of 900 km/h. What is the power developed by the engine?

25 MW

If both mass and velocity of a ball are tripled, the kinetic energy is increased by a factor of:

27

Old Faithful geyser in Yellowstone Park shoots water hourly to a height of 40 m. With what velocity does the water leave the ground?

28 m/s

A Hooke's law spring is compressed a distance d and is used to launch a particle of mass m vertically to a height h above its starting position. Under double the compression, the spring is now used to launch a particle of mass 2 m. How high does the second mass rise above its starting position?

2h

A 100-W light bulb is left on for 10.0 hours. Over this period of time, how much energy was used by the bulb?

3 600 000 J

A 10.0-kg box starts at rest and slides 3.5 m down a ramp inclined at an angle of 10 with the horizontal. If there is no friction between the ramp surface and crate, what is the velocity of the crate at the bottom of the ramp? (g = 9.8 m/s2)

3.5 m/s

A simple pendulum, 2.0 m in length, is released by a push when the support string is at an angle of 25 degrees from the vertical. If the initial speed of the suspended mass is 1.2 m/s when at the release point, to what maximum angle will it move in the second half of its swing?

30 degrees

By how much is the energy stored in a Hooke's law spring increased when its stretch is increased from 8.00 cm to 16.0 cm?

300 %

A professional skier reaches a speed of 56 m/s on a 30 degree ski slope. Ignoring friction, what was the minimum distance along the slope the skier would have had to travel, starting from rest?

320 m

A 2 000-kg ore car rolls 50.0 m down a frictionless 10.0 incline. If there is a horizontal spring at the end of the incline, what spring constant is required to stop the ore car in a distance of 1.00 m?

340 kN/m

A 1 200-kg automobile moving at 25 m/s has the brakes applied with a deceleration of 8.0 m/s2. How far does the car travel before it stops?

39 m

A 20-N crate starting at rest slides down a rough 5.0-m long ramp, inclined at 25 with the horizontal. 20 J of energy is lost to friction. What will be the speed of the crate at the bottom of the incline?

4.7 m/s

A pile driver drives a post into the ground. The mass of the pile driver is 2 500 kg and it is dropped through a height of 8.0 m on each stroke. If the resisting force of the ground is 4.0 106 N, how far is the post driven in on each stroke?

4.9 cm

A 1 000-kg sports car accelerates from zero to 25 m/s in 7.5 s. What is the average power delivered by the automobile engine?

41.7 kW

A baseball catcher puts on an exhibition by catching a 0.15-kg ball dropped from a helicopter at a height of 101 m. What is the speed of the ball just before it hits the catcher's glove 1.0 m above the ground? (g = 9.8 m/s2 and ignore air resistance)

44 m/s

A parachutist of mass 50.0 kg jumps out of an airplane at a height of 1 000 m. The parachute deploys, and she lands on the ground with a speed of 5.0 m/s. How much energy was lost to air friction during this jump?

489 000 J

Water flows over a section of Niagara Falls at a rate of 1.20 106 kg/s and falls 50.0 m. What is the power dissipated by the waterfall?

588 MW

A Hooke's law spring is compressed a distance d and is used to launch a mass m vertically to a height h above its starting position. Under double the compression, the spring is now used to launch the mass. How high does the mass now rise above its starting position?

4h

A speed boat requires 80 kW to move at a constant speed of 15 m/s. What is the resistive force of the water at this speed?

5 300 N

A 50-N crate is pulled up a 5-m inclined plane by a worker at constant velocity. If the plane is inclined at an angle of 37 to the horizontal and there exists a constant frictional force of 10 N between the crate and the surface, what is the force applied by the worker?

50 N

The net force acting on a 6.0-kg object is given by Fx = (10 x) N, where Fx is in newtons and x is in meters. How much work is done on the object as it moves from x = 0 to x = 10 m?

50J

A bobsled makes a run down an ice track starting at 150 m vertical distance up the hill. If there is no friction, what is the velocity at the bottom of the hill?

54 m/s

Preston pushes a wheelbarrow weighing 500 N to the top of a 50.0-m ramp, inclined at 20.0 with the horizontal, and leaves it. Tamara accidentally bumps the wheelbarrow. It slides back down the ramp, during which an 80.0-N frictional force acts on it over the 50.0 m. What is the wheelbarrow's kinetic energy at the bottom at of the ramp? (g = 9.8 m/s2)

550 J

A 60-kg woman runs up a flight of stairs having a rise of 4.0 m in a time of 4.2 s. What average power did she supply?

560 W

A golf ball hits a wall and bounces back at 3/4 the original speed. What part of the original kinetic energy of the ball did it lose in the collision?

7/16

What is the minimum amount of energy required for an 80-kg climber carrying a 20-kg pack to climb Mt. Everest, 8 850 m high?

8.67 MJ

A baseball outfielder throws a baseball of mass 0.15 kg at a speed of 40 m/s and initial angle of 30. What is the kinetic energy of the baseball at the highest point of the trajectory? Ignore air friction.

90 J

A horizontal force of 100 N is applied to move a 45-kg cart across a 9.0-m level surface. What work is done by the 100-N force?

900 J

A worker pushes a sled with a force of 40 N over a level distance of 6.0 m. If a frictional force of 24 N acts on the wheelbarrow in a direction opposite to that of the worker, what net work is done on the wheelbarrow?

96 J

A 10.0-kg sled slides down a snowy hill. At position A it is moving at 1.00 m/s. when it reaches position B it is moving at 3.00 m/s. Finally it passes position C moving at 1.00 m/s again. Position C is 3.00 m lower than position A and 1.00 m lower than position B.The coefficient of kinetic friction varies from place to place in the snow. What is the work done by friction on the sled as it moves from A to C?

?

The work done by static friction can be:

Any of the above: positive, negative, zero.

If during a given physical process the only force acting on an object is friction, which of the following must be assumed in regard to the object's kinetic energy?

It cannot be determined from the infor- mation given.

In a problem using energy considerations to solve for the speed of a ball thrown from the top of a building when it strikes the ground below, where should the potential energy have its zero value?

It doesn't matter since only differences in potential energy matter in solutions.

The unit of work, joule, is dimensionally the same as:

N*m

The SI units for k, the spring constant, are equivalent to:

Newton/meter

When an object is dropped from a tower, what is the effect of the air resistance as it falls

None of the above choices are valid: increases the object's potential energy, increases the object's kinetic energy, & does positive work

Instantaneous Power

P = F v

Equation of Power

P = W/t

Elastic Potential Energy

PE = 1/2kx^2

Equation of Potential Energy

PE= mgy

A student has to work the following problem: A block is being pulled along at constant speed on a horizontal surface a distance d by a rope supplying a force F at an angle of elevation θ. The surface has a frictional force acting during this motion. How much work was done by friction during this motion? The student calculates the value to be -Fdsinθ. How does this value compare to the correct value?

The answer cannot be found until it is known whether θ is greater than, less than, or equal to 45°

A block is projected with speed v across a horizontal surface and slides to a stop due to friction. The same block is then projected with the same speed v up an incline where is slides to a stop due to friction. In which case did the total mechanical energy of the block decrease the least?

The case on the inclined surface had the least decrease in total mechanical energy.

Three different mass projectiles are launched from the top of a building each at different angles of elevation. Each particle has the same initial kinetic energy. Which particle has the greatest kinetic energy just as it impacts with the ground?

The one with the highest mass.

Three different mass projectiles are launched from the top of a building each at different angles of elevation. Each particle has the same initial kinetic energy. Which particle has the greatest speed just as it impacts with the ground?

The one with the lowest mass.

Two blocks are released from the top of a building. One falls straight down while the other slides down a smooth ramp. If all friction is ignored, which one is moving faster when it reaches the bottom?

They both will have the same speed.

SI unit of Power

W or J/s or Kgm^2/s^3

Work-kinetic energy theorem

Wnet = delta-KE

As an object is lowered into a deep hole in the surface of the earth, which of the following must be assumed in regard to its potential energy?

decrease

Which of the following is an example of a nonconservative force?

friction

Initial vertical height of the pendulum

h = l (1 + cos(theta))

A Hooke's law spring is compressed a distance d and is used to launch a mass m vertically to a height h above its starting position. Under the same compression d, the spring is now used to launch a mass of 2m. How high does this second mass rise?

h/2

A force of 5.0 N is applied to a 20-kg mass on a horizontal frictionless surface. As the speed of the mass increases at a constant acceleration, the power delivered to it by the force:

increases

The unit of power, watt, is dimensionally the same as:

joule/second.

Which of the following is that form of energy associated with an object's motion?

kinetic

Which of the following is that form of energy associated with an object's location in a conservative force field?

potential

The rate at which work is done is equivalent to which of the following?

power

The quantity of work equal to one joule is also equivalent to which of the following?

watt/s

The area under the force vs. displacement curve represents:

work

Is it possible for the total mechanical energy of a moving particle to be negative?

yes