Determine the force required to move the body, up the inclined with constant velocity.

Sample Solution

Here's how to determine the force required to move the body up the inclined plane with constant velocity:

1. Identify the forces acting on the body: There are three main forces acting on the body:

   • Weight (W): 50 N acting straight down due to gravity.
   • Normal force (N): A force exerted by the inclined plane on the body, perpendicular to the plane's surface.
   • Friction force (F_f): 29 N acting parallel to the inclined plane surface, opposing the motion (upward in this case).

2. Resolve the weight force (W) into components: We need to break down the weight force (W) into two components:

   • W_x: Acting parallel to the inclined plane (causing the body to slide down).
   • W_y: Acting perpendicular to the inclined plane (balanced by the normal force).

W_x = W * sin(theta) (where theta is the angle of inclination, 30° in this case) W_x = 50 N * sin(30°) W_x = 50 N * 0.5 W_x = 25 N (acting downwards)

W_y = W * cos(theta) W_y = 50 N * cos(30°) W_y = 50 N * 0.866 W_y = 43.3 N (acting upwards)

Full Answer Section

3. Balance the forces in the vertical direction: The normal force (N) balances the vertical component of the weight (W_y) to prevent the body from sinking into the plane. N = W_y N = 43.3 N (acting upwards)

4. Determine the net force required to overcome friction: To move the body with constant velocity (neither accelerating nor decelerating), we need to overcome the frictional force (F_f). Net force = Force required to move the body (F) Net force = Force to overcome friction (F_f)

5. Since the body moves with constant velocity, the net force is zero. Therefore, the force required to move the body (F) needs to exactly cancel out the frictional force (F_f). F = F_f F = 29 N (acting upwards)

Conclusion: The force required to move the body up the inclined plane with constant velocity is 29 N, acting upwards and parallel to the inclined plane surface.