# Experiment relationship between force and extension of a spring

### BBC Bitesize - GCSE Physics (Single Science) - Forces and elasticity - AQA - Revision 4

This strong fit lends credibility to the results of the experiment. This relationship between the force applied to a spring and the amount of stretch was first discovered in by Translated from Latin, this means "As the extension, so the force. The force needed to stretch or compress a spring is proportional to its change in The directly proportional relationship is between extension and force, not. Add another 10 g mass and record the new spring length. Take away the previous spring length from the new length to calculate the extension (the difference).

That would have been stupid. Instead, like every sensible person since Galileo, he placed a sheet of white paper several inches in front of the eyepiece and looked at the projected image of the sun. Such a device is called a helioscope. Robert Hooke He then went on to list ten inventions and discoveries he had made. This was not followed by any later list with the remaining inventions he promised, by the way.

- Motion of a Mass on a Spring
- What is Hooke's Law?

These included a way to regulate pendulum clocks, a method for constructing arches, and other inventions in optics, hydraulics, and mechanical engineering. The third item on his list is of importance to us right now.

**Hooke's Law Physics, Basic Introduction, Restoring Force, Spring Constant, Practice Problems**

And the way of computing the velocity of Bodies moved by them. If this is not carefully attended to and there are generally many quantities that could affect the results of an experiment the experimental results will be worthless.

Of course, there are some secondary but still very important purposes for this lab.

We aren't really spending a whole lab period "discovering" something that has already been known for hundreds of years What sort of result - what sort of answer - would a physicist expect in an experiment? The very best result would be an equation that expresses the mathematical relationship between the two quantities involved in the experiment. In this case, the very best result would be an equation that expresses the mathematical relationship between force and stretch for a typical spring.

So, how do you "come up" with such an answer? As you proceed in your study of physics you will learn some techniques that generally turn a graph into an equation with a minimum of fuss. So, if you have a set of graphs that show the relationship between force and stretch for typical springs, you are pretty-much "golden". How do you get these graphs? You need to know how much force produces how much stretch - for as wide a range of force and stretch as possible.

Clearly, you need to measure both the stretching force and the amount of stretch - how much known forces stretch a spring. Now the glider begins to move to the right of point C. As it does, the spring force acts leftward upon the rightward moving glider. This restoring force causes the glider to slow down during the entire path from position C to position D to position E. Sinusoidal Nature of the Motion of a Mass on a Spring Previously in this lessonthe variations in the position of a mass on a spring with respect to time were discussed.

At that time, it was shown that the position of a mass on a spring varies with the sine of the time. The discussion pertained to a mass that was vibrating up and down while suspended from the spring. The discussion would be just as applicable to our glider moving along the air track.

If a motion detector were placed at the right end of the air track to collect data for a position vs. Position A is the right-most position on the air track when the glider is closest to the detector. The labeled positions in the diagram above are the same positions used in the discussion of restoring force above.

You might recall from that discussion that positions A and E were positions at which the mass had a zero velocity.

## Forces and elasticity

Position C was the equilibrium position and was the position of maximum speed. If the same motion detector that collected position-time data were used to collect velocity-time data, then the plotted data would look like the graph below.

Observe that the velocity-time plot for the mass on a spring is also a sinusoidal shaped plot. The only difference between the position-time and the velocity-time plots is that one is shifted one-fourth of a vibrational cycle away from the other. Also observe in the plots that the absolute value of the velocity is greatest at position C corresponding to the equilibrium position.

The velocity of any moving object, whether vibrating or not, is the speed with a direction.

### Springs – The Physics Hypertextbook

The magnitude of the velocity is the speed. The direction is often expressed as a positive or a negative sign. In some instances, the velocity has a negative direction the glider is moving leftward and its velocity is plotted below the time axis. In other cases, the velocity has a positive direction the glider is moving rightward and its velocity is plotted above the time axis. You will also notice that the velocity is zero whenever the position is at an extreme.

This occurs at positions A and E when the glider is beginning to change direction. So just as in the case of pendulum motionthe speed is greatest when the displacement of the mass relative to its equilibrium position is the least. And the speed is least when the displacement of the mass relative to its equilibrium position is the greatest. Energy Analysis of a Mass on a Spring On the previous pagean energy analysis for the vibration of a pendulum was discussed. Here we will conduct a similar analysis for the motion of a mass on a spring.

In our discussion, we will refer to the motion of the frictionless glider on the air track that was introduced above. The glider will be pulled to the right of its equilibrium position and be released from rest position A.