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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?