Question

In the first figure, a block of mass m lies on a horizontal frictionless surface and is attached to one end of a horizontal spring (spring constant k) whose other end is fixed. The block is initially at rest at the position where the spring is unstretched (x = 0) when a constant horizontal force in the positive direction of the x axis is applied to it. A plot of the resulting kinetic energy of the block versus its position x is shown in the second figure. The scale of the figure's vertical axis is set by K_s = 6.0 J. (a) What is the magnitude of F? (b) What is the value of k?

Answer 1

The magnitude of the applied force can be found using the Work-Energy theorem, while the value of the spring constant can be determined using the formula for potential energy stored in a spring.

Step-by-step explanation:

To find the magnitude of the applied force, we can use the Work-Energy theorem. The potential energy stored in the spring when the block is released is equal to the work done by the applied force. From the graph, we can see that the potential energy is 6.0 J when the block is at x = A. Therefore, the magnitude of the applied force is equal to the potential energy divided by the displacement, F = 6.0 J / A.

To find the value of the spring constant, we can use the formula for potential energy stored in a spring, U = 1/2 k x^2. From the graph, we can see that the potential energy is 6.0 J when the block is at x = A. Plugging in the values, we get 6.0 J = 1/2 k A^2. Rearranging the equation, we find the value of the spring constant, k = (2 * 6.0 J) / A^2.