Final answer:
The net force on a block at the bottom of a friction less loop-the-loop is the sum of its weight and the force needed for centripetal acceleration, total resulting in a net force of 3mg, which means the answer is c) 3/2 * m * g.
Step-by-step explanation:
The concerns a small block of mass m sliding along a friction less loop-the-loop, seeking the magnitude of the net force acting on it at the bottom of the loop. To find the net force, we can use Newton's second law, which states that the net force is equal to mass times acceleration (Fnet = ma). At the bottom of the loop, the block has two forces acting on it: the gravitational force (mg) acting downward and the normal force from the track acting upward.
which is what provides the centripetal force necessary for the block to move in a circular path. At the bottom of the loop, the acceleration is centripetal, meaning that it acts towards the center of the circular path. This requires the net force to be greater than just the weight of the block.
Specifically, the net force is the sum of gravitational force and the force providing centripetal acceleration. The speed of the block at the bottom of the loop can be found using energy conservation from the top to the bottom, and it turns out that the block will have a speed such that the centripetal force is equal to the block's weight (mg).