Question

A person pushes on a box in the East direction with 8

N of force, another person pushes on the same box
south with 20 N of force. What force (magnitude and
direction) would a third person need to push on the
crate so that the box is in equilibrium?
Magnitude of the third
vector is
Direction of third
vector is
✓ [Choose ]
46.40 N
28.00 N
21.54 N
21.8° South of East
21,8° North of West
68.2° South of East
68.2° North of West

Answer 1

In order for the box to be in equilibrium, the third person's force should be equal but opposite in direction to the resultant force of the two forces already acting on the box.

First, let's calculate the resultant force acting on the box. The box is being pushed with 8 N to the east and 20 N to the south. Since these forces are at right angles to each other, we can use the Pythagorean theorem to find the magnitude of the resultant force:

Magnitude = sqrt((8 N)^2 + (20 N)^2)

= sqrt(64 N^2 + 400 N^2)

= sqrt(464 N^2)

= 21.54 N

The direction of the resultant force can be calculated using trigonometry. Specifically, we can use the tangent function, which is the ratio of the opposite side to the adjacent side in a right triangle.

tan(θ) = Opposite/Adjacent

tan(θ) = 20 N / 8 N

θ = atan(20/8)

θ = 68.2°

The direction of the force is therefore 68.2° South of East (since we have taken East as the base direction and South as the angle direction).

The third person should therefore apply a force of 21.54 N in the direction exactly opposite to 68.2° South of East, which is 68.2° North of West.

So, the correct choices are:

Magnitude of the third vector is 21.54 N.

Direction of third vector is 68.2° North of West.