A horizontal force is applied to a block of mass that is in contact with a smooth…
PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Force and Translational Dynamics · Force and Translational Dynamics
Problem
A horizontal force P is applied to a block of mass m that is in contact with a smooth plane inclined at an angle θ to the horizontal. The force P acts horizontally (parallel to the ground) and the block remains at rest relative to the plane.
(i) Resolve all the forces acting on the block into components perpendicular to the plane and write the condition for equilibrium in that direction.
(ii) Hence obtain an expression for the normal reaction N in terms of m, g, P, and θ.
(iii) If m=4kg, θ=30∘, and the required normal reaction is 21mg, calculate the magnitude of P.
(iv) Using your result in (ii), discuss quantitatively how the normal reaction varies with the applied horizontal force for a fixed angle θ. Illustrate the nature of this dependence with appropriate reasoning.