Embedded Files
objectives
objectives
Calculating Potential Energy
Calculating Potential Energy
- The ball below has potential energy because of the Earth's gravitational pull | on it and its position above the ground.
- This is called gravitational potential energy (PE). If the ball falls, it gains kinetic energy (KE). Both PE and KE can be calculated.
- The gravitational potential energy of the ball on the left is equal to the work which would be done if the ball were to fall to the ground. Assuming no air resistance, it is also equal to the work done in lifting the ball a distance h up from the ground in the first place:
- downward force on ball = weight of ball = mg
- So: upward force needed to lift ball = mg
- So: work done in lifting ball - force X distance moved = mgh
- For an object of mass m at a vertical height h above the ground:
Gravitational potential energy = mgh
- For example, if a 2 kg mass is 3 m above the ground, and g is 10 N/kg: ; gravitational PE = 2 kg X 3rn X 10 N/kg = 60 J
Calculating Kinetic Energy
Calculating Kinetic Energy
Units
- Mass is measured in kilograms (kg).
- Force is measured in newtons (N). Weight is a force.
- Work is measured in joules (J). Energy is measured in joules (J).
Scalar Energy
Scalar Energy
- Energy is a scalar quantity: it has magnitude (size) but no direction. So you do not have to allow for direction when doing energy calculations.
- On the right, objects A and B have the same mass and are at the same height 1 above the ground. B was lifted vertically but A was moved up a smooth slope.
- Although A had to be moved further, less force was needed to move it, and j the work done was the same as for B. As a result, both objects have the same PE.
- The PE (mgh) depends on the vertical gain in height h and not on the particular path taken to gain that height.
KE & PE Problems
KE & PE Problems
Example: If the stone on the right is dropped, what is its kinetic energy when it has fallen half-way to the ground? (g = 10 N/kg)
- In problems like this, you don’t necessarily have to use KE = ½mv2.
- When the stone falls, its gain in KE is equal to its loss in PE, so you can calculate that instead:
- height lost by stone = 2 m
- So: gravitational PE lost by stone = mgh = 4 kg X 10 N/kg X 2 m = 80 J
- So: KE gained by stone = 80 J
As the stone started with no KE. this is the stone's KE half-way down.
Example: The stone on the right slides down a smooth slope. What is its speed when it reaches the bottom? (g = 10 N/kg)
- This problem can also be solved by considering energy changes.
- At the top of the slope, the stone has extra gravitational PE.
- When it reaches the bottom, all of this PE has been transformed into KE.
- gravitational PE at top of slope = mgh
- = 4 kg X 10 N/kg X5m = 200 J
- So: kinetic energy at bottom of slope = 200 J
- So: ½mv2 = 200 J
- So: ½ X 4 kg X v2 = 200 J
- This gives: v =10 m/s
- So the stone s speed at the bottom of the slope is 10 m/s.
- Note: if the stone fell vertically, it would start with the same gravitational PE and end up with the same KE, so its final speed would still be 10 m/s.
calculating ke & pe worksheet
calculating ke & pe worksheet
Please complete the worksheet below and hand in on google classroom
4.03---Calculating-PE-and-KE.docxPage updated
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