A theater stage crew needs to roll a heavy -pound lighting rig up to a stage platform that is feet high. They can build either a steep ramp that is feet long or a gentle ramp that is feet long. Assuming the ramp surfaces and wheels are perfectly frictionless, which of the following statements correctly compares the two ramp options?
- AThe -foot ramp reduces both the required effort force and the total work done by half compared to the -foot ramp.
- BThe -foot ramp requires less total work than the -foot ramp because the lighting rig is moved across a shorter total distance.
- The -foot ramp requires half the effort force of the -foot ramp, but the total work done remains exactly the same for both.Answer
- DThe -foot ramp requires less effort force because placing the rig on a shallower angle effectively reduces the mass of the rig.
Answer
The -foot ramp requires half the effort force of the -foot ramp, but the total work done remains exactly the same for both.
The Ideal Mechanical Advantage (IMA) of an inclined plane is its length divided by its height. The -foot ramp has an IMA of (), requiring lbs of effort force. The -foot ramp has an IMA of (), requiring lbs of effort force. Therefore, the longer ramp requires half the effort force. However, because simple machines do not change the total amount of work done (), both ramps require ft-lbs of total work to lift the rig feet vertically.
Step-by-Step Solution
Key Concept
Ideal Mechanical Advantage and the Work-Force Tradeoff