1401 Energy

A 2 kg glider is released from rest at the top of a frictionless 30 degree inclined plane. The speed of the glider has been measured at several locations as the car moves down the plane. 1. Use GPE = mgh to calculate heights. 2. Use ½ mv2 to calculate KEs. 3. Calculate ME = GPE + KE.

Mass m = 2 kg g = 10N/kg

h (m) / GPE (J) / Speed (m/s) / KE (J) / Mech. Energy (J)
h = GPE/mg / mgh / measured / ½ mv2 / GPE + KE
1.25 / 25 / 0 / 0 / 25
1.2 / 24 / 1 / 1 / 25
1.05 / 21 / 2 / 4 / 25
0.8 / 16 / 3 / 9 / 25
0.45 / 9 / 4 / 16 / 25
0 / 0 / 5 / 25 / 25

As the glider descends, the ______GPE______decreases

As the glider descends, the ____ speed____ and ______KE______are both increasing.

As the glider descends, the _____Mechanical Energy______stays the same.

If friction were present on the incline, the measured speed values would be __less___ than the values in the table above.

If friction were present on the incline, the mechanical energy of the system would be ___ less ______than the values in the table above.


2. A 100kg object is released from rest at a height of 2.0m on a frictionless ramp and slides downward. Calculate the KE and speed of the object when it is at a height of 1.0m. Repeat for when it is at 0.0m. Does the shape of the ramp matter? Explain. Would the speeds be the same if the object were dropped? Does the mass matter? Recalculate the speed at height 0.0m if 400J are converted to thermal energy during the slide.

Location1 is height 2.0m. Location 2 is height 1.0m. Location 3 is height 0m. Conservation of energy (without elastic and thermal energies):

The shape of the ramp does not matter since there is no friction. The speeds are identical for an object dropped from 2.0m height. The speeds are mass independent since there is no friction and no elastic energy.

When friction is present thermal energy is created. If 400J of thermal energy are created, there will be that much less KE at the end of the slide.

The speed is lower due to the friction. The mass does matter when thermal energy is created.

3. A 55kg child is swinging on a swing with length 3.0m. When the child stops the swing makes an angle of 80 degrees from vertical. Calculate the speed of the child at the bottom of the swing. Assume no thermal energy is created.

First calculate the height at the top of the swing above the lowest point of the swing.

4. A 30kg box comes off a ramp with a speed of 6m/s and slides along a level surface with a coefficient of kinetic friction of 0.32. How far does the box slide before stopping?

The box will stop once all the original KE is converted to thermal.


5. A 1kg object is thrown at a speed of 20m/s. Calculate the work done on the object by the person who throws it. If the person throwing used 2m distance to accelerate the object, what average force was exerted on the object?

Use the Work-Energy Theorem:

To calculate the average force, use the definition of work and assume the force is in the direction of motion and that only the throwing force is doing work (i.e. a level throw).

This would be a hard throw to make.

6. An arrow mass 26grams (400 grains) is shot from a bow at 76m/s (250fps). Calculate the work done on the arrow. Calculate the average force exerted on the arrow if the bow used 80cm to accelerate the arrow.

Repeat the procedure from the previous problem.


7. A 2kg object is projected horizontally from an ideal spring with a speed of 15m/s. The spring was originally compressed a distance of 10cm. Calculate the spring constant of the spring. Assume no thermal energy is created.

Use Energy conservation (without thermal).

/ 1 / 2
/ 0 / 0
/ 0 /
/ / 0
thermal / 0 / 0
Total / /

8. A 100kg person steps on a bathroom scale, causing it to compress by 3mm. Calculate the spring constant of the spring assuming it is an ideal spring.

Use Energy conservation (without thermal). GPE is converted into elastic PE.

/ 1 / 2
/ 0 /
/ 0 / 0
/ 0 /
thermal / 0 / 0
Total / 0 /