Chapter 7, Problem 95P

(a)

To determine

To prove:For a block attached to a vertical spring, its potential energy can be represented as a function of position as $U=\frac{1}{2}k{y}^2-mgy$ .

(b)

To determine

To graph:

The values of potential energy $U$ relative to the position $y$ .

(c)

To determine

To Explain:From the graph (Figure 1 in part (b)) that there exists a position of stable equilibrium for a positive value for y and determine the value of y when the block is in the equilibrium position.

(d)

To determine

The force acting on the system for any value of y , from the equation $U=\frac{1}{2}k{y}^2-mgy$ .

(e)

To determine

The maximum value reached by the block if it is released at the unstressed position and also indicate it on the graph.