Work, Power, and Energy

Honors Physics

Work

Work changes an object’s energy

This is a dot product, meaning…

W= 𝐹𝑑𝑐𝑜𝑠(if there is an angle between F and d)

Units: Joules

1 Nm = 1 Joule

𝑊 = റ𝐹 ∙ റ𝑑

Example

A 50 kg crate is dragged along a floor for 5 meters with a force of 60 N. The rope makes an angle of 30 above the horizontal. How much work was done on it by the applied force?

a) 0 N

b) 250 N

c) 260 N

d) 300 N

Power

The rate at which work is done

The rate of energy transfer

Power measures how quickly

work is done

Units: Watts

1 Watt = 1 Joule per second

𝑃 =𝑊𝑜𝑟𝑘

𝑡

Example

A crane lifts a 900 kg car vertically upward at a constant speed to a height of 15 meters in 45 seconds.

a) How much work is done on the car?

b) Calculate the power output of the motor.

Example

A 40-kilogram student runs up a staircase to a floor that is 5.0 meters higher than her starting point in 7.0 seconds. The student’s power output is

a) 29 W

b) 280 W

c) 1.4 × 103 W

d) 1.4 × 104 W

Potential Energy

𝑃𝐸 = 𝑚𝑔ℎ

Generally, potential energy is the energy an object has by virtue of its position in a system

Gravitational potential energy is a result of an object’s height above Earth

A result of the work done to lift an object against gravity

Kinetic Energy

The energy an object has by virtue of its motion and its velocity

Units: Joules 𝐾𝐸 =1

2𝑚𝑣2

Example

Calculate the gravitational potential energy a 2500 kg roller coaster has at the top of a 9 meter hill.

Calculate the kinetic energy a 0.050 kg bullet has when traveling 380 m/s.

Example

The gravitational potential energy, with respect to Earth, that is possessed by an object is dependent on the object’s

a) acceleration

b) momentum

c) position

d) speed

Example

As a ball falls freely toward the ground, its potential energy

a) decreases

b) increases

c) remains the same

Justification???

Example

As a ball falls freely toward the ground, its kinetic energy

a) decreases

b) increases

c) remains the same

Justification???

Springs

Hooke’s law

k = spring constant (in N/m) ; this is a measure of how “stiff” or “slinky” the spring is

x = the distance the spring is stretched or compressed

𝐹 = 𝑘𝑥

Springs

Elastic potential energy is the stored energy in a stretched or compressed spring

Example: energy stored in spring loaded nerf gun

Units: Joules

𝑃𝐸 =1

2𝑘𝑥2

Example

A 2.0 kg mass is placed on the end of a spring and the spring stretches a distance of 0.8 meters.

What is the spring constant of the spring?

If the same spring were stretched to 1.5 meters, how much energy would be stored in the spring?