Explain why the output work for any machine cant be greater than the input work

Agymnast dismounts off the uneven bars in a tuck position with a radius of 0.3m (assume she is a solid sphere) and an angular velocity of 2rev/s. during the dismount she stretches out into the straight position, with a length of 1.5m, (assume she is a uniform rod through the center) for her landing. the gymnast has a mass of 50kg. what is her angular velocity in the straight position?

Given the position vector of the particle r(t)=(t+1)i+(t^2−1)j+2t k, find the particle's velocity and acceleration vectors at t=1

It's a snowy day and you're pulling a friend along a level road on a sled. you've both been taking physics, so she asks what you think the coefficient of friction between the sled and the snow is. you've been walking at a steady 1.5m/s, and the rope pulls up on the sled at a 32 ∘ angle. you estimate that the mass of the sled, with your friend on it, is 65 kg and that you're pulling with a force of 80 n .