Calculating Spring Force: A Physics Challenge

How can we calculate the spring force exerted on a mass at the top of an incline?

Given a mass of 7 kg moving down a circular ramp, traveling over surfaces with friction and inclines, and coming to rest on a spring with a spring constant of 4000 N/m, what is the spring force exerted on the mass in Newtons?

Answer:

The spring force exerted on the mass at the top of the last incline can be calculated by equating the potential energy to gravitational potential energy and solving for the spring force. The spring force exerted on the mass is 320 N.

To calculate the spring force exerted on the mass at the top of the last incline, we can use the equation for potential energy: PE = 1/2kx^2, where k is the spring constant and x is the displacement. The mass at the top of the incline has come to rest, so the kinetic energy is zero and all the initial energy is converted to potential energy.

Therefore, we have PE = mgH, where m is the mass, g is the acceleration due to gravity, and H is the height. By equating these two expressions for potential energy, we can solve for the spring force. In this case, the spring force exerted on the mass is 320 N.

By understanding the principles of potential energy, gravity, and Hooke's Law, we can effectively calculate the spring force exerted on a mass at the top of an incline. This physics challenge showcases the application of these concepts in real-world scenarios.