Work, Energy, and Simple Machines: questions with answers

A force does work only when the object moves. The bag stays at rest, so its displacement is zero. Then $W = F s \cos\theta = 40 \times 0 = 0$ J. The height above the floor and the time held do not add any work.

Friction acts opposite to the displacement, so $\theta = 180^\circ$ and $\cos 180^\circ = -1$. Then $W = F s \cos\theta = 20 \times 3 \times (-1) = -60$ J.

Kinetic energy is $\tfrac{1}{2}mv^2$. Squaring the speed gives $3 \times 3 = 9$. Then $\tfrac{1}{2} \times 2 \times 9 = 9$ J.

Kinetic energy is $\tfrac{1}{2}mv^2$. Replacing $v$ by $2v$ gives $\tfrac{1}{2}m(2v)^2 = 4 \times \tfrac{1}{2}mv^2$. So the kinetic energy becomes four times as large.

Height is measured from the chosen zero level. The table top is that level, so h=3 m. PE=mgh=2×10×3=60 J.

Gravity transfers energy between the two mechanical forms without dissipative loss.

Power is work divided by the time taken. Here $P = 600 \div 3 = 200$ W.

In the ideal case the work put in equals the work got out, so $F \times L = W \times h$. The ramp length $L$ is greater than the rise $h$, so the force $F$ is smaller than the weight $W$. The machine trades force for distance; it neither creates energy nor returns more work than it receives.