Question

200N of force due to gravity are acting on a box that is being pushed with a force of 85N up a ramp that forms a 35° angle with the floor. What is the magnitude and direction of the resultant force on the box?

(a) Magnitude: 48.82N, Direction: 35°
(b) Magnitude: 85N, Direction: 35°
(c) Magnitude: 138.52N, Direction: 68.07°
(d) Magnitude: 48.82N, Direction: 68.07°

Answer 1

The magnitude of the resultant force on the box is 248.82N, and its direction is 35°.

Step-by-step explanation:

To find the magnitude and direction of the resultant force on the box, we need to break down the forces acting on it. The force due to gravity, which is acting vertically downward, has a magnitude of 200N. The force that is being applied to push the box up the ramp has a magnitude of 85N.

Using trigonometry, we can find the vertical component of the force being applied up the ramp. The vertical component equals 85N multiplied by the sine of the angle of the ramp (35°). This gives us a value of 48.82N.

Therefore, the magnitude of the resultant force is the sum of the vertical component of the applied force (48.82N) and the force due to gravity (200N), which equals 248.82N. The direction of the resultant force is the same as the angle of the ramp, which is 35°.