Question

There is a free body diagram drawn on a block on a 50-degree incline with 3 force vectors. The first vector is pointing away from the surface of the incline and perpendicular to the surface, labeled F Subscript N Baseline. The second vector is pointing into and perpendicular to the surface of the incline, labeled F Subscript g y Baseline. The third vector is pointing straight down to the center of the earth, labeled F Subscript g Baseline. There is another force parallel to the surface of the incline and down the hill starting at the tip of the F Subscript g y Baseline vector, labeled F Subscript g x Baseline.
A box with a mass of 100.0 kg slides down a ramp with a 50 degree angle.

What is the weight of the box?
N

What is the value of the normal force? Round the answer to the nearest whole number.

N

What is the acceleration of the box? (Disregard friction and air resistance.) Round the answer to the nearest tenth.

m/s2

Answer 1

Weight: W = mg = (100.0 kg)(9.8 m/s^2) = 980 N

Normal force: N = mg cosθ = 980 cos(50°) ≈ 980(0.6428) ≈ 629.9 → 630 N (nearest whole number)

Acceleration down the ramp (no friction): a = g sinθ = 9.8 sin(50°) ≈ 9.8(0.7660) ≈ 7.5 m/s^2 (to the nearest tenth)