Question

The section ab is one quadrant of a circle of radius 2.0 m and the spring constant of the spring is 435n/m. If the entire track is frictionless, how far will the spring be compressed if the block is released from rest at point a?

Answer 1

The spring will not be compressed if the block is released from rest at point A.

Step-by-step explanation:

To determine how far the spring will be compressed when the block is released from rest at point A, we need to apply the concepts of spring force and potential energy. The force exerted by the spring can be calculated using Hooke's Law: F = kx, where F is the force, k is the spring constant, and x is the displacement from equilibrium. In this case, the block is released from rest, so it initially has no kinetic energy. The potential energy stored in the spring will be converted into the kinetic energy of the block as it compresses the spring. Therefore, we can equate the potential energy of the spring to the kinetic energy of the block: 0.5kx² = 0.5mv². Rearranging the equation, we have x = sqrt((mv²)/(k)). Plugging in the given values, we have x = sqrt((3.0 kg * 0 m/s) / (435 N/m)) = 0 m.