Question

From the rest, a box of mass 20kg was pulled a frictionless horizontal floor with a force of 100N acting at an angle of 30^° over a distance of 10m in its vertical component of force. step by step explain all with calculation.​

a) 100N
b) 150N
c) 86.6N
d) 173.2N

Answer 1

The vertical component of the force is 50N, determined by the sine function as it is the component opposite the angle of the applied force. Since the force is vertical and the displacement is horizontal, no work is done by the vertical component.

Step-by-step explanation:

The question involves calculating the vertical component of force exerted on a box over a frictionless horizontal surface. To find the vertical component of the 100N force at a 30° angle, we use the sine function, since it is opposite the angle in the right-angle triangle formed by the force vector.

The vertical component (Fy) is calculated as follows:

1. Fy = F × sin(θ)
2. Fy = 100N × sin(30°)
3. Fy = 100N × 0.5
4. Fy = 50N

This vertical force of 50N acts upwards and does no work on the box since the box is on a horizontal surface and the force is not causing any displacement in the vertical direction. The work done by the vertical component of the force over a horizontal distance would be zero, since work is calculated by the formula W = F × d × cos(φ), where φ is the angle between the force direction and the displacement direction, which in this case is 90°, making the cosine term zero.