Using a spring attached to a vertical support, develop an experimental procedure

Question

Using a spring attached to a vertical support, develop an experimental procedure to determine the spring constant for the spring hanging from the vertical support using a spring, a set of weights with hangers, and a motion sensor. Your method should stretch the spring by no more than 5 centimeters. Describe this method in detail. Because this is being determined from experimental data, which strategies or approaches will you use to get the most accurate value possible for this particular spring's spring constant? Explain your reasoning explicitly. Do not assume your instructor knows anything. Every spring has a spring constant (k). The spring constant is determined by dividing the magnitude of the force that causes an expansion of the spring by the amount that the spring expands. k = Delta F/d.

Explanation / Answer

It's a very simple method.

As per hookes' law, F = kx ( where F = weight of hanging mass, and x is the stretch in the spring)

Place the motion detector below the mass ( varying mass)

Let decide three postions:

1) No mass, measure the unstretched length of the spring.

2) Now hang , a light mass ( m). on placing the mass

Note the upstretched length of the spring, the motion detector will detect the height of bottom of spring with respect to ground.

Now, hang a light mass with spring, the motion detector will measure the height (Hl) with respect to ground and you can calculate the stretch in the spring (Xl)

Now, hang a heavy mass with spring. Again, the motion sensor will detect the height of mass (Hh) with respect to ground on equilibrium. Now, again you can find the stretch in the spring (Xh).

Plot the values in the equation,

F = kx for both the experiments, and you can find spring constant.

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