Question

A boy is exerting a force of 70 N at a 50-degree angle on a lawnmower. He is accelerating at 1.8 m/s2. Round the answers to the nearest whole number.
What is the mass of the lawnmower?
What is the normal force exerted on the lawnmower?

Answer 1

The lawnmower accelerates in the positive horizontal direction, so that the net horizontal force is, by Newton's second law,

(70 N) cos(-50°) = m (1.8 m/s²)

where m is the mass of the lawnmower. Solve for m :

m = ((70 N) cos(-50°)) / (1.8 m/s²)

m ≈ 25 kg

The lawnmower presumably doesn't get lifted off the ground, so that the net vertical force is 0. If n is the magnitude of the normal force, then by Newton's second law,

n - m g + (70 N) sin(-50°) = 0

n = m g + (70 N) sin(50°)

n = (25 kg) (9.8 m/s²) + (70 N) sin(50°)

n ≈ 300 N