Potential And Kinetic Energy Worksheet (Page 17 of 29) in pdf

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8.2 Efficiency and Energy

8.2

Efficiency describes how well energy is converted from one form into another. A process is 100% efficient if no

energy is “lost” due to friction, to create sound, or for other reasons. In reality, no process is 100% efficient.

Efficiency is calculated by dividing the output energy by the input energy. If

Output energy (J)

Efficiency =

you multiply the result by 100, you will get efficiency as a percentage. For

Input energy (J)

example, if the answer you get is 0.50, you can multiply by 100 and write

your answer as 50%.

You drop a 2-kilogram box from a height of 3 meters. Its speed is 7 m/s when it hits the ground. How efficiently

did the potential energy turn into kinetic energy?

Looking for

Solution

You are asked to find the efficiency.

(2 kg)(9.8 m/s )(3 m) 58.8 J

Given

(1 / 2)(2 kg)(7 m/s)

49 J

The mass is 2 kilograms, the height is 3 meters,

and the landing speed is 7 m/s.

The input energy is the potential energy, and the

output energy is the kinetic energy.

Relationships

Kinetic energy = 1/2mv

Efficiency (49 J)/(58.8 J) 0.83 or 83%

Potential energy = mgh

The efficiency is 0.83 or 83% (0.83 × 100).

Efficiency = (output energy)/(input energy)

Engineers who design battery-operated devices such as cell phones and MP3 players try to make them as

efficient as possible. An engineer tests a cell phone and finds that the batteries supply 10,000 J of energy to

make 5500 J of output energy in the form of sound and light for the screen. How efficient is the phone?

What’s the efficiency of a car that uses 400,000 J of energy from gasoline to make 48,000 J of kinetic

energy?

A 1000.-kilogram roller coaster goes down a hill that is 90. meters tall. Its speed at the bottom is 40. m/s.

What is the efficiency of the roller coaster? Assume it starts from rest at the top of the hill.

What do you think happens to the “lost” energy?

Use the concepts of energy and efficiency to explain why the first hill on a roller coaster is the tallest.

You see an advertisement for a new free fall ride at an amusement park. The ad says the ride is 50. meters tall

and reaches a speed of 28 m/s at the bottom. How efficient is the ride? Hint: You can use any mass you wish

because it cancels out.

Imagine that you are working as a roller coaster designer. You want to build a record-breaking coaster that

goes 70.0 m/s at the bottom of the first hill. You estimate that the efficiency of the tracks and cars you are

using is 90.0%. How high must the first hill be?

Potential And Kinetic Energy Worksheet Page 17

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