A homeowner pushes a lawn mower across a horizontal patch of grass with a constant speed by applying a force P. The arrows in the diagram correctly indicate the directions but not necessarily the magn

Question

A homeowner pushes a lawn mower across a horizontal patch of grass with a constant speed by applying a force P. The arrows in the diagram correctly indicate the directions but not necessarily the magnitudes of the various forces on the lawn mower. Which of the following relations among the various force magnitudes, $W, f, N, P$ is CORRECT?

TestHub · Accepted Answer

Constant speed, so the net force is zero. The push $P$ acts along the handle, at angle $θ$ to the vertical, directed down and toward the mower.

Horizontal: $P sin θ = f \Rightarrow f < P$ .

Vertical: $N = W + P cos θ \Rightarrow N > W$ .

So $P > f$ and $N > W$ : option (A).

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