Download Gravitational potential energy and more Study notes Physics in PDF only on Docsity!
Gravitational
potential
energy
Objectives
- Investigate examples of gravitational potential energy.
- Calculate the potential energy, mass, or height of an object using the gravitational potential energy equation.
- Choose the reference frame and coordinate system best suited to a particular problem.
- What does each of the symbols mean in this equation: EP = mgh?
- Translate the equation EP = mgh into a sentence with the same meaning.
- How much EP does a 1 kg mass gain when raised by a height of 10 m?
- How high would a 2.0 kg mass have to be raised to have a gravitational potential energy of 1,000 J?
- Mountain climbers at the Everest base camp (5,634 m above sea level) want to know the energy needed reach the mountain’s summit (altitude 8,848 m). What should they choose as zero height for their energy estimate: sea level, base camp, or the summit?
Assessment
- Which location is most convenient to choose as the zero height reference frame if the robot tosses the ball into the hole?
Assessment
Physics terms
- potential energy
- gravitational potential energy
- mechanical energy
Equations
The change in gravitational potential energy of an object is its mass multiplied by g and by the change in height. At Earth’s surface, g = 9.8 N/kg, or 9.8 kg m/s^2 or
Gravitational potential energy
This heavy container has been raised up above ground level. Due to its height, it has stored energy —gravitational potential energy. How do we know that the energy is there?
Gravitational potential energy
This heavy container has been raised up above ground level. Due to its height, it has stored energy —gravitational potential energy. If the container is released, the stored energy turns into kinetic energy.
Gravitational potential energy
If the mass of the container increases, its potential energy will also increase. If the height of the container increases, its potential energy will also increase.
Gravitational potential energy
The gravitational potential energy of an object is...
Gravitational potential energy
m
m
The gravitational potential energy of an object is the mass m in kilograms.. .x
Gravitational potential energy
g
g
The gravitational potential energy of an object is the mass m in kilograms multiplied by the local acceleration due to gravity g (which is 9.8 m/s^2 near Earth’s surface)...
Work is force times distance.
W = Fd
Deriving the formula
W = Fd
F = mg
Deriving the formula
To lift an object, you must exert an upward force equal to the object’s weight. Work is force times distance.
W = Fd
F = mg d = h
The distance you lift it is the height h.
Deriving the formula
Work is force times distance.
W = Fd = mgh = Ep
F = mg
force = weight distance = height
d = h
Deriving the formula
Work is force times distance.
An example
A 1.0 kg mass lifted 1.0 meter gains 9.8 joules of gravitational potential energy. Click this interactive calculator on page 259
Exploring the ideas
Engaging with the concepts
What is the potential energy of a 1.0 kg ball when it is 1.0 meter above the floor?
Grav. potential energy 1.0 1.
Engaging with the concepts
What is the potential energy of a 1.0 kg ball when it is 1.0 meter above the floor? Ep = 9.8 J (^) 9. Grav. potential energy 1.0 1. What is the energy of the same ball when it is 10 m above the floor?
Engaging with the concepts
What is the potential energy of a 1.0 kg ball when it is 1.0 meter above the floor? Ep = 9.8 J (^) 9. Grav. potential energy 1.0 10 What is the energy of the same ball when it is 10 m above the floor? Ep = 98 J 98
Engaging with the concepts
How does the potential energy of a 10 kg ball raised 10 m off the floor, compare to the 1 kg ball?
Grav. potential energy 10 10
Engaging with the concepts
How does the potential energy of a 10 kg ball raised 10 m off the floor, compare to the 1 kg ball?
Grav. potential energy It is 10 times greater,^98010 1. or 980 J.
Engaging with the concepts
Suppose a battery contains 500 J of energy. What is the heaviest object the battery can raise to a height of 30 meters? (^) 9. Mass 30 10 500
Reference frames and
coordinate systems
When calculating kinetic energy, you need to chose a reference frame.
- Typically, we choose the Earth as our reference frame.
- We treat the Earth as if it is at rest. When calculating gravitational potential energy, we need to choose where to put the origin of our coordinate system. In other words, where is height equal to zero?
Reference frames and
coordinate systems
Where is zero height?
Determining height
Where is zero height? the floor? the ground outside? the bottom of the hole?
Determining height
Determining height
If h = 1.5 meters, then the potential energy of the ball is 14.7 joules.
Determining height
If h = 4 meters, then the potential energy is 39.2 J.
Determining height
If h = 6 meters, then the potential energy is 58.8 J.
14.7 J? 39.2 J? 58.8 J?
Which answer is correct?
Which is correct?
Which is correct?
14.7 J? 39.2 J? 58.8 J?
All are correct! The height you use depends on the problem you are trying to solve …
How do you choose?
How do you choose?
The height you use depends on the problem you are trying to solve … … because only the change in height actually matters when solving potential energy problems. So how do you know where h = 0?
How do you choose?
Gravitational potential energy is always defined relative to your choice of location for zero height. And unlike kinetic energy, it can even be negative!
Reference frames Does the path matter?
A set of identical twins wants to get to the top of a mountain.
- One twin hikes up a winding trail.
- The second twin takes the secret elevator straight to the top. Which twin has the greatest potential energy at the top?
Path independence
The twins have the SAME potential energy at the top. It doesn’t matter HOW they gained height. Changes in potential energy are independent of the path taken.
Assessment
- What does each of the symbols mean in this equation: EP = mgh?
Assessment
- What does each of the symbols mean in this equation: EP = mgh? m = mass in kg g = the strength of gravity in N/kg h = the change in height in meters
- Translate the equation EP = mgh into a sentence with the same meaning.
Assessment
- What does each of the symbols mean in this equation: EP = mgh? m = mass in kg g = the strength of gravity in N/kg h = the change in height in meters
- Translate the equation EP = mgh into a sentence with the same meaning. The change in gravitational potential energy of an object is its mass multiplied by g and multiplied by the change in height.
- How much EP does a 1 kg mass gain when raised by a height of 10 meters?
Assessment
- What does each of the symbols mean in this equation: EP = mgh? m = mass in kg g = the strength of gravity in N/kg h = the change in height in meters
- Translate the equation EP = mgh into a sentence with the same meaning. The change in gravitational potential energy of an object is its mass multiplied by g and multiplied by the change in height.
- How much EP does a 1 kg mass gain when raised by a height of 10 meters? EP = mgh = 98 joules
Assessment
- How high would a 2 kg mass have to be raised to have a gravitational potential energy of 1,000 J?
Assessment
- How high would a 2 kg mass have to be raised to have a gravitational potential energy of 1,000 J? h = EP/mg = 51 m
- Mountain climbers at the Everest base camp (5,634 m above sea level) want to know the energy needed reach the mountain’s summit (altitude 8,848 m). What should they choose as zero height for their energy estimate: sea level, base camp, or the summit? 4. How high would a 2 kg mass have to be raised to have a gravitational potential energy of 1,000 J? h = EP/mg = 51 m 5. Mountain climbers at the Everest base camp (5,634 m above sea level) want to know the energy needed reach the mountain’s summit (altitude 8,848 m). What should they choose as zero height for their energy estimate: sea level, base camp, or the summit? The climbers are located at the base camp, so their change in gravitational potential will be relative to the base camp. They should therefore set the base camp s altitude as zero height.
Assessment
Assessment
- Which location is most convenient to choose as the zero height reference frame if the robot tosses the ball into the hole? 6. Which location is most convenient to choose as the zero height reference frame if the robot tosses the ball into the hole? Setting h = 0 at the lowest place that the object reaches means the potential energy will always be positive. This makes the problem easier to solve.
Assessment
h = 0 m
