Question

If a simple machine could be frictionless, how would its IMA and
AMA compare?
4. Compare the effects of a fixed pulley and a movable pulley on the
size and direction of the input force.
5. In a compound machine made up of two simple machines, how is
the work output of the first simple machine related to the work
input of the second simple machine?

Answer 1

1. If a simple machine were frictionless, its ideal mechanical advantage (IMA) would equal its actual mechanical advantage (AMA).
Reason: no energy is lost, so input work = output work. F_in · d_in = F_out · d_out ⇒ F_out/F_in = d_in/d_out, so AMA = IMA.

4. Fixed pulley vs movable pulley:
- Fixed pulley: changes the direction of the input force (for example, pull down to lift up) but does not reduce the magnitude of the input force. IMA ≈ 1 (AMA ≈ 1).
- Movable pulley: reduces the required input force (a single movable pulley gives IMA = 2, so the input force is about half the load) but does not change the direction of the applied force on the load itself. (Direction of the rope can still be arranged differently using additional pulleys.)

5. In a compound machine of two simple machines, the output work of the first machine becomes the input work of the second: W_out1 = W_in2 (neglecting losses). With friction/losses, W_out1 < W_in1, and therefore W_in2 = W_out1 < W_in1.