Download Work and Energy

WORK & ENERGY
Work
Work Energy Thm.
Kinetic Energy
Power
Potential Energy
Conservation of Energy
WORK & ENERGY
• Work: Transfer of energy through motion
• Energy: Ability to cause Change
• Kinetic Energy: Energy Due to Motion
• For work to be done, a force must be exerted for a distance
• A component of force must be parallel to motion
WORK & ENERGY
• WORK:
𝑊 = 𝐹 ∙ 𝑑 = 𝐹𝑑𝑐𝑜𝑠ϴ
• (Scaler Dot Product)
• F*d = 1N *1m = 1 Joule
WORK & ENERGY (examples)
• An athlete pulls a 100kg sled a distance of 10m with a force of 320N
at an angle of 15o above the horizontal. How much work does he do?
Some dude carries a 4 kg briefcase a distance of 4m at a constant speed. How much work
does he do on the briefcase?
WORK & ENERGY (examples)
• A weight lifter raises a 100kg weight a distance of 2m at constant speed. How much work does he
do?
• A weight lifter raises a 100 kg weight a distance of 2m at constant speed. How much work does
gravity do?
• A weight lifter holds a 100 kg weight a distance of 2m above the ground. How much work is being
done?
WORK & ENERGY THEOREM
Sum of all work done on an object equals change in Kinetic Energy
Σ𝑊 = ∆𝐾𝐸
𝑣𝑓2 = 2𝑎𝑑 + 𝑣𝑖2
2𝑎𝑑 = 𝑣𝑓2 − 𝑣𝑖2
𝑣𝑓2 − 𝑣𝑖2
𝑎𝑑 =
2
𝑣𝑓2 − 𝑣𝑖2
𝑚 𝑎𝑑 = 𝑚𝑎 𝑑 = 𝐹𝑑 = (𝑚)
2
1
1
2
𝐹𝑑 = 𝑚𝑣𝑓 − 𝑚𝑣𝑖2
2
2
1
𝐾𝐸 = 𝑚𝑣2
2
Positive work done by person on shovel
(Adds Energy to the system)
Negative work done by friction on shovel
(Removes Energy from the system)
WORK & ENERGY THEOREM EXAMPLES
• An athlete pulls a 100kg sled a distance of 10m with a force of 320N
at an angle of 15o above the horizontal. What is final velocity of the
mass?
W=3091J
WORK & ENERGY THEOREM EXAMPLES
A Bow exerts a force of 200N on a 0.150kg
arrow for a distance of 0.60m.
What is the final velocity of the arrow?
WORK & ENERGY THEOREM EXAMPLES
• A weight lifter raises a 100 kg weight a distance of 2m at constant speed. How much work does
he do?
• A weight lifter raises a 100 kg weight a distance of 2m at constant speed. How much work does
gravity do?
• A weight lifter holds a 100 kg weight a distance of 2m above the ground. How much work is
being done?
• A weight lifter holds a 100 kg weight a distance of 2m above the ground. What is the final
velocity of the weights?
WORK & ENERGY THEOREM EXAMPLES
A 1200 kg car moving at 15m/s skids to a stop in 20m.
• How much work required to stop the car?
• What is the coefficient of friction between the tires and the road?
POWER
Power = Rate at which work is done
𝑊𝑜𝑟𝑘 𝑊 𝐹𝑑
𝑃𝑜𝑤𝑒𝑟 =
=
=
= 𝐹𝑣 = 𝐹𝑣𝑐𝑜𝑠𝜃
𝑇𝑖𝑚𝑒
𝑡
𝑡
𝐽
1 = 1 𝑤𝑎𝑡𝑡 = 1𝑊
𝑠
1𝐻𝑝 = 746 𝑊𝑎𝑡𝑡𝑠
Power
A weight lifter raises a 100 kg weight a distance of 2m at constant speed in 1.5
seconds. What is his power output?
An athlete pulls a 100kg sled a distance of 10m in 5.5s with a force of 320N at an
angle of 15o above the horizontal. What is the power output?
Power
• Example: An Elevator can lift a maximum of 900kg at a rate of 1.5m/s.
What is the power of the elevator
POWER
Example: A 1500kg car can accelerate from 0-60mph in 3.8s. How
much power does the car exert?
POWER
• How much weight can a 5 Hp motor lift 2m in 10 seconds?
• How many joules of energy does a 60 Watt light bulb use in one hour?
POTENTIAL ENERGY
• Potential Energy = Energy stored due to position (Stored Energy)
• Electric Potential Energy = energy due to position of electrons.
• Chemical Potential Energy = energy due to position of molecules.
• Nuclear Potential Energy = Energy stored due to position of Protons and Neutrons
Gravitational Potential Energy
• Energy due to position on a gravitational field
• Gravity can cause an object to fall
• Gravity has the ability to do work on an object
• The amount of work gravity can do is equal to the amount of potential
energy
𝑊 = 𝐹𝑑 = 𝑚𝑔 ℎ → 𝐺𝑃𝐸 = 𝑚𝑔ℎ=Ug
Elastic Potential Energy
• Energy stored in the shape of an object
• As the shape of an object changes, it has the ability to do work in
order to return to its original position
•
•
•
•
Stretching a rubber band
Compressing a Spring
Bending a Ruler
Pole Vaulting
Elastic Potential Energy
• Hooke’s Law: Force required to stretch Ideal spring
• k= spring constant, x = displacement from rest position.
• Work done on spring = 𝑤 = 12𝑘𝑥2
• Elastic Potential Energy = Work done on Spring
𝐸𝑃𝐸 = 12𝑘𝑥2
Conservation of Energy
• Total energy of a closed system remains constant.
• Energy cannot be created or destroyed, it only changes forms
𝐾𝐸1 + 𝑈1 = 𝐾𝐸2 + 𝑈2
Conservation of Energy
A 150 kg rollercoaster car initially at rest rolls down a 50m hill.
a) How much work was done to get the car to the top of the hill?
b) How fast will it be moving at bottom of the hill?
c) How fast will the car be moving at the top of the second hill 25m
high?
Conservation of Energy
• A sling shot is stretched a distance of 2.5m with a force of 300N.
• What is the spring constant of the sling shot?
• How much work was done on the sling shot?
• How fast will a 2.0kg water balloon be moving after it is fired horizontally
from the slingshot?
• If it is shot in the vertical direction, How high will it go?
Conservation of Energy
A high jumper run at a speed of 8 m/s, and jumps to height of 2.5m.
What is his velocity at maximum height?
What could be his maximum height?
Conservation of Energy
• Mass of bear = 50kg
• Height Bear falls
• Spring displacement = 0.75m
• Spring constant k of trampoline?