Question

A rock of mass (m) is attached to a string of length (r). The rock is swung in a circular motion, and at the low point of its swing, it has a speed (v_b). Determine the force that the string exerts on the rock. Express your answer in terms of (v_b), (r), (m), and the constant (g).

a) ( F = fracm ⋅ v_b^2/r + mg )

b) ( F = fracm ⋅ v_b^2/r - mg )

c) ( F = fracm ⋅ v_b^2/r )

d) ( F = fracm ⋅ v_b/r )

Answer 1

The force exerted by the string on the rock at the lowest point of the swing is the sum of gravitational and centripetal forces, and is given by the expression ( F = fracm × v_b^2/r + mg ).

Step-by-step explanation:

To determine the force that the string exerts on the rock when it is swung in a circular motion and is at the low point of its swing with a speed (v_b), we must consider two forces: the gravitational force (weight of the rock) and the centripetal force necessary to keep the rock moving in a circle.

The gravitational force is equal to the mass of the rock (m) times the acceleration due to gravity (g), so it equals m × g. The centripetal force required for circular motion is equal to the mass of the rock times the square of the tangential velocity divided by the radius of the circle (v_b^2/r).

At the lowest point in the swing, both gravitational force and centripetal force act in the same direction towards the center of the circle. Therefore, the total force exerted by the string is the sum of these two forces, which is given by m × v_b^2/r + m × g. Thus, the correct expression for the force that the string exerts on the rock is ( F =frac m × v_b^2/r + mg ).