Question

The force required to stretch a slingshot by different amounts is shown in the graph on the right.

A) what is the spring constant of the spring?
B) How much work does a child need to do to stretch the sling 15 cm from equilibrium?

Answer 1

The spring constant can be found by calculating the slope of the force versus displacement graph, and the work done to stretch the sling can be calculated using the formula (1/2) * k * (displacement)^2.

Step-by-step explanation:

The spring constant, also known as the force constant or stiffness, measures how much force is needed to stretch or compress a spring. It is represented by the symbol k and is calculated as the ratio of the force applied to the displacement produced. In this case, we can determine the spring constant by finding the slope of the force versus displacement graph provided. The slope of a straight line is given by the formula:

slope = (change in y-axis)/(change in x-axis)

To find the spring constant of the slingshot, we need to determine the change in force and change in displacement for any two points on the graph and use the slope formula to calculate the spring constant.

To find the work done to stretch the sling 15 cm from equilibrium, we can use the formula:

work done = (1/2) * k * (displacement)^2

Substitute the given values and calculate the work done.

Answer 2

The spring constant is found by rearranging Hooke's Law and using the work done by a spring formula. The work to stretch the slingshot 15 cm from equilibrium is calculated using the work calculation for springs once the spring constant is known.

Step-by-step explanation:

The spring constant k is a measure of the stiffness of a spring and it dictates the amount of force required to compress or extend the spring by a certain distance. According to Hooke's Law, F = kx, where F is the force applied, k is the spring constant, and x is the displacement from the equilibrium position.

To calculate the spring constant using the given information, we can rearrange Hooke's Law to solve for k: k = F / x. As per the example provided, if it takes 500 J of work to compress a spring 10 cm (0.1 m), we use energy work done by a spring formula W = 1/2 k x^2, which results in k = 2W / x^2. Thus, k = 2 * 500 J / (0.1 m)^2 = 100000 N/m.

For part b), to calculate the work done to stretch a slingshot 15 cm from equilibrium, we use the same work formula: W = 1/2 k x^2. Once we know the spring constant, we can substitute k and x into this formula to find the work.