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- Homework Statement
- find experimentally and theoretically the horizontal distance a slingshot which roughly obeys Hooke's Law will shoot a projectile.

- Relevant Equations
- F=kx (x = distance stretched), range = v*(sin(2A))/g, (v = velocity upon leaving slingshot, A = angle to horizontal of v, g = acceleration due to gravity); v = x*sqrt(2k/m) , (m=mass of projectile,)

This concerns an elementary experiment that I (a teacher) have done with several secondary school classes, up until now with success. However, I gave the same instructions to a homeschooling student (in another country , so I couldn’t actually directly oversee the experiment), and the experiment’s results were off by a factor of two to the predictions by the tried-and-true calculations. Naturally it is difficult to check something like this from afar, but perhaps someone can suggest reasons for which the experiment was so far off.

The experiment makes a large simplification, which admittedly is strictly not valid but has always served as a decent approximation. The assumption is that the rubber strip in a slingshot roughly obeys Hooke’s Law.

The experiment is then

(a) find a value for k in Hooke’s Law F=kx experimentally by hanging several weights to it (but careful not to use weights which were too heavy) versus the length this stretches the rubber band (including the length of stretch that one will use to shoot) to shoot a projectile . From the straight-line graph (force versus stretch distance) one obtains the spring constant.

(b) Measure the angle A to the horizontal that one will shoot the projectile of mass m, and the length x' that one will stretch the rubber band in the same way as was done in (a).

(c) shoot the projectile (several times) , and measure the horizontal distance D (from the slingshot) that it lands.

(d) calculate the theoretical horizontal distance D’ (in steps, rather than a single formula, but that is irrelevant) from the measured k, x', m and A.

Usually D and D’ are pretty close, despite ignoring friction, heat loss, and other minor influences. (I did not see any undue friction in her experimental set-up.)

I checked the student’s calculations, and they were correct.

I also see no problem in measuring the restoring force in a vertical position although the shooting takes place at an angle.

The projectile’s weight of 23 grams seemed to me to be appropriate.

The most likely candidate for a problem is in the value of k. The student’s graph for k indicates that the rubber strip is following Hooke’s Law quite closely. I did have her calculate k a second time after performing the experiment, and indeed it had changed quite a bit (rubber stretches), but even using this new, lower k her calculated D’ was twice the value of her measured D.

My first instinct is to have her measure/calculate k several times to see what sort of variability k might have for the rubber strip.

However, if that doesn’t help --- what am I missing?

Thanks for any suggestions.

The experiment makes a large simplification, which admittedly is strictly not valid but has always served as a decent approximation. The assumption is that the rubber strip in a slingshot roughly obeys Hooke’s Law.

The experiment is then

(a) find a value for k in Hooke’s Law F=kx experimentally by hanging several weights to it (but careful not to use weights which were too heavy) versus the length this stretches the rubber band (including the length of stretch that one will use to shoot) to shoot a projectile . From the straight-line graph (force versus stretch distance) one obtains the spring constant.

(b) Measure the angle A to the horizontal that one will shoot the projectile of mass m, and the length x' that one will stretch the rubber band in the same way as was done in (a).

(c) shoot the projectile (several times) , and measure the horizontal distance D (from the slingshot) that it lands.

(d) calculate the theoretical horizontal distance D’ (in steps, rather than a single formula, but that is irrelevant) from the measured k, x', m and A.

Usually D and D’ are pretty close, despite ignoring friction, heat loss, and other minor influences. (I did not see any undue friction in her experimental set-up.)

I checked the student’s calculations, and they were correct.

I also see no problem in measuring the restoring force in a vertical position although the shooting takes place at an angle.

The projectile’s weight of 23 grams seemed to me to be appropriate.

The most likely candidate for a problem is in the value of k. The student’s graph for k indicates that the rubber strip is following Hooke’s Law quite closely. I did have her calculate k a second time after performing the experiment, and indeed it had changed quite a bit (rubber stretches), but even using this new, lower k her calculated D’ was twice the value of her measured D.

My first instinct is to have her measure/calculate k several times to see what sort of variability k might have for the rubber strip.

However, if that doesn’t help --- what am I missing?

Thanks for any suggestions.