Answer key: Energy on a Ramp Worksheet
For teachers. This page is hidden from search engines and not linked from student pages, but it is not password-protected, so please don’t share the link with students. Student worksheet: Energy on a Ramp Worksheet.
Goal: Track how gravitational potential energy turns into kinetic energy on a frictionless ramp, and test whether the ramp angle or the mass changes the speed at the bottom.
Completed results table
| Setting | Height | Speed | Kinetic energy | Potential energy |
|---|---|---|---|---|
| Top of the 30° ramp | 5 m | 0 m/s | 0 J | 98.1 J |
| Halfway down in height | 2.5 m | 7.004 m/s | 49.05 J | 49.05 J |
| Bottom of the 30° ramp | 0 m | 9.905 m/s | 98.1 J | 0 J |
| Gentle ramp (15°), bottom | 0 m | 9.905 m/s | 98.1 J | 0 J |
| Steep ramp (60°), bottom | 0 m | 9.905 m/s | 98.1 J | 0 J |
| Double the mass (4 kg), bottom | 0 m | 9.905 m/s | 196.2 J | 0 J |
Answers
Add the kinetic and potential energy in each 2 kg row. What do you notice?
The total is always 98.1 J, the starting potential energy mgh₀ = 2 × 9.81 × 5. On a frictionless ramp energy only changes form; at 2.5 m it is split equally, 49.05 J each.
Did the ramp angle change the speed at the bottom? Explain why or why not.
No. All three ramps give 9.905 m/s at the bottom, because speed depends only on the drop in height: mgh = ½mv², so v = √(2gh) = √(2 × 9.81 × 5). A steeper ramp only gets the block there sooner.
Doubling the mass doubled one bottom reading but not the other. Which one, and why?
The kinetic energy doubled to 196.2 J, because both potential and kinetic energy are proportional to mass. The speed stayed 9.905 m/s, because mass cancels out of mgh = ½mv².
At half the height, is the block moving at half its final speed? Use your table.
No. At 2.5 m it moves at 7.004 m/s, about 71% of 9.905 m/s, not 50%. Half the energy has become kinetic energy, and speed grows with the square root of kinetic energy.
Predict, then test: what speed will the block reach at the bottom if it starts 10 m high (twice as high)?
14.007 m/s, about 1.41 times faster, not twice as fast. Doubling the height doubles the energy (196.2 J for the 2 kg block), and speed grows with the square root of energy.
This model has no friction. What would change on a real ramp?
Friction would transfer some energy to thermal energy, so the kinetic energy at the bottom would be less than 98.1 J and the speed less than 9.905 m/s. Energy is still conserved overall; it just doesn’t all stay as kinetic and potential energy.