problem: you push a heavy crate down a ramp at a constant velocity. only four forces act on the crate. which…

Explanation:

Step1: Identify forces acting on the crate

The four forces are gravity ($F_g$), normal force ($F_n$), push force ($F_p$), and friction ($F_f$).

Step2: Determine work done by each force

Normal force is perpendicular to displacement, so $W_n = 0$. Gravity and push force do positive work ($W_g, W_p > 0$). Friction opposes motion, doing negative work ($W_f < 0$).

Step3: Apply the Work-Energy Theorem

Constant velocity means $\Delta K = 0$. Thus, net work is zero: $W_{net} = W_g + W_p + W_f = 0$.

Step4: Compare magnitudes of work

Since $W_g + W_p + W_f = 0$, it follows that $|W_f| = |W_g + W_p|$. Therefore, the magnitude of work done by friction must be greater than the magnitude of work done by gravity or the push force individually.

Answer:

(d) The force of friction.