A 110.0 kg box is pushed by a horizontal force F at constant speed up a frictionless ramp which makes an angle of 35.0 deg with the horizontal. Find the magnitude of the applied force F.
(component of the force in the direction of motion)*(distance moved, L) = Work = (Increase in potential energy)
F*cos35*L = M*g*L*sin 35
F = M g tan35 = 755 N
A man pushes on a piano with mass 150 so that it slides at constant velocity down a ramp that is inclined at 14.7 above the horizontal floor. Neglect any friction acting on the piano.
To find the magnitude of the applied force F, we can use the concept of forces and equilibrium.
1. Draw a diagram: Draw a diagram showing the box on the ramp, with all relevant forces labeled.
2. Identify the forces: Identify all the forces acting on the box. In this case, we have the weight of the box (mg), the normal force (N), and the applied force (F).
3. Resolve the force components: Resolve the weight force (mg) into its components parallel and perpendicular to the ramp. The weight force can be broken down into two components: the force acting parallel to the ramp (mg*sinθ) and the force acting perpendicular to the ramp (mg*cosθ), where θ is the angle of the ramp.
4. Apply Newton's second law: Apply Newton's second law in the direction parallel to the ramp. Since the box is moving at a constant speed, the net force in this direction must be zero. Therefore, the applied force F must be equal in magnitude but opposite in direction to the force acting parallel to the ramp (mg*sinθ).
5. Calculate the magnitude of F: Substitute the values into the equation F = mg*sinθ. Given that the mass (m) of the box is 110.0 kg and the angle (θ) of the ramp is 35.0 degrees, we can calculate the magnitude of F.
F = (110.0 kg) * (9.8 m/s^2) * sin(35.0 deg)
= 569.84 N
Therefore, the magnitude of the applied force F is approximately 569.84 Newtons.