Guy has to get a piano onto a 2.4 m high platform. He can use a 3.0 m long frictionless ramp or a 4.0 m long frictionless ramp. Which ramp will Guy use if he wants to do the least amount of work?
Either ramp as the work done is same in both cases.
The shorter ramp will require less work.
The longer ramp will require less work.
Either ramp as the work done is same in both cases.
To determine which ramp Guy will use to do the least amount of work, we need to consider the concept of work in physics.
Work is defined as the force applied to an object multiplied by the distance the object moves in the direction of that force. In this case, Guy needs to apply a force to lift the piano onto the platform, and the distance he needs to move it is the vertical height of the platform.
Now let's compare the two ramps:
1. The 3.0 m long ramp:
If Guy uses the 3.0 m long ramp, the horizontal distance he needs to push the piano will be shorter. However, the vertical distance he needs to lift the piano will remain the same (2.4 m). This means that Guy will have to exert a larger force to move the piano up the steeper inclined ramp.
2. The 4.0 m long ramp:
If Guy uses the 4.0 m long ramp, the horizontal distance he needs to push the piano will be longer. But the advantage is that the inclined ramp will be shallower, requiring a smaller force to move the piano up the ramp. However, the total distance Guy needs to push the piano will be slightly longer.
In this case, the ramp that Guy should use to do the least amount of work is the longer 4.0 m ramp. Despite the slightly longer pushing distance, the reduced force required to lift the piano up the shallower ramp will result in less total work being done.
So, to minimize the work required, Guy should use the 4.0 m long frictionless ramp.