Question 1

Which physical principle is primarily used to determine the initial velocity $$v_0 of $$the steel ball as it leaves the spring gun?

Accepted Answer

Conservation of energy

Question 2

Given the equation $$\$$\frac{1}{2}$$kX^2$$ - \mu mgl = \frac{1}{2}$$mv_0^2$$\$$\$$, what does the term $$\$$\mu mgl\$$\$$ represent in the context of the spring gun experiment?

Accepted Answer

The energy lost due to friction as the ball moves through the channel

Question 3

If the spring constant $$k is $$increased while keeping all other variables constant, what will be the effect on the horizontal range $$R of $$the steel ball?

Accepted Answer

The range $$R$$ will increase

Question 4

Why is it important to take multiple shots for each trigger setting and analyze the spread of the landing positions?

Accepted Answer

To account for and analyze random errors in the experiment

Question 5

Which of the following best describes the relationship you should plot to determine the spring constant $$k$$ and friction coefficient $$\mu$$ from your data?

Accepted Answer

Plot $$R^2 vs$$ $$X^2$$

Question 6

If the coefficient of friction $$\mu is $$not negligible, how does it affect the calculated value of the spring constant $$k if $$ignored in the analysis?

Accepted Answer

The calculated $$k$$ will be too high

Question 7

A student finds that the measured range $$R is $$consistently shorter than predicted by the frictionless model. What is the most likely explanation?

Accepted Answer

The coefficient of friction $$\mu is $$significant and was not accounted for

Question 8

Given the simplified equation $$\R = X$$ \sqrt{\frac{2hk}{mg}}\$$\ ($$when friction is negligible), what is the physical meaning of the slope in a plot of $$R vs$$ $$X$$?

Accepted Answer

It is equal to $$\sqrt{\frac{2hk}{mg}}$$

Question 9

In the context of this experiment, why is it important to keep the paper strip taped to the floor until all measurements are complete?

Accepted Answer

To avoid introducing erroneous displacements in the measured range

Question 10

Suppose the mass of the steel ball is doubled while all other parameters remain constant. How does this affect the horizontal range $$R ($$assuming friction is negligible)?

Accepted Answer

The range $$R$$ will decrease by a factor of $$\sqrt{2}$$

Question 11

Which of the following is a valid reason for using a straight-line fit to the $$R^2 vs$$ $$X^2$$ data?

Accepted Answer

Because the theoretical model predicts $$R^2 is $$proportional to $$X^2$$ when friction is considered

Question 12

If the spring gun is not clamped firmly to the table, what type of error is most likely to be introduced?

Accepted Answer

Systematic error due to consistent misalignment

Question 13

A student plots $$R^2 vs$$ $$X^2$$ and finds a non-zero intercept. What could this indicate about the experiment?

Accepted Answer

There is energy loss due to friction or other non-ideal effects

Question 14

Which of the following best explains why the steel ball follows a parabolic trajectory after leaving the spring gun?

Accepted Answer

The ball is acted on only by gravity and its initial horizontal velocity

Question 15

If the height $$h of $$the table is increased, what is the effect on the horizontal range $$R ($$assuming all other variables are constant and friction is negligible)?

Accepted Answer

The range $$R$$ will increase

Lab Techniques: The Range of a Spring Gun – Experimental Design, Data Analysis, and Error Considerations

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