No questions found
In this experiment, you will investigate the extension of a spring.
(a) You have been provided with a spring.
• Measure and record the length $x_0$ of the unstretched coiled section of the spring, as shown in Fig. 1.1.
$x_0 =$ ..........................................................[1]
(b) • Set up the apparatus as shown in Fig. 1.2.
The protractor should be attached to the wooden block using some of the Blu-Tack.
The height of the rod of the clamp above the bench should be approximately 35 cm.
One loop of the spring should be around the rod of the clamp.
The other loop of the spring should be around the rod of stand B close to the top of the rod and secured using Blu-Tack.
• Slide the base of stand B until the angle between the rod of stand B and the stretched spring is 90°.
• The length of the coiled section of the spring is $x$.
The angle between the rod of stand B and the horizontal is $\theta$.
Measure and record $x$ and $\theta$.
$x =$ ..........................................................
$\theta =$ ..........................................................
• Calculate $e$ where
$$e = (x - x_0).$$
$e =$ .........................................................[1]
(c) Change the height of the boss. Slide the base of stand B until the angle between the rod of stand B and the stretched spring is again 90°.
Measure and record $x$ and $\theta$. Repeat until you have six sets of values.
Record your results in a table. Include values of $e$, $\frac{e}{\cos \theta}$ and $\tan \theta$ in your table.
[10]
(d) (i) Plot a graph of $\frac{e}{\cos \theta}$ on the $y$-axis against $\tan \theta$ on the $x$-axis.
[3]
(ii) Draw the straight line of best fit.
[1]
(iii) Determine the gradient and $y$-intercept of this line.
gradient = ..........................................................
y-intercept = ..........................................................
[2]
(e) It is suggested that the quantities $e$ and $\theta$ are related by the equation
$$\frac{e}{\cos \theta} = N \tan \theta + M$$
where $N$ and $M$ are constants.
Using your answers in (d)(iii), determine the values of $N$ and $M$.
Give appropriate units.
$N =$ ..........................................................
$M =$ ..........................................................
[2]
600
503
564
(a) (i) You have been provided with two lengths of string. Measure and record the diameter $d$ of the thicker string.
d = ........................................................... mm [2]
(ii) Estimate the percentage uncertainty in your value of $d$.
percentage uncertainty = ..............................................................[1]
(iii) Calculate the cross-sectional area $A$ of the string using
$A = \frac{\pi d^2}{4}$.
A = .................................................................[1]
(iv) Justify the number of significant figures that you have given for your value of $A$.
.............................................................................................
.............................................................................................
.............................................................................................[1]
(b) (i) You have been provided with two mass hangers and a pulley.
• Rotate the pulley to ensure that it rotates freely.
• Using the thicker string, set up the apparatus as shown in Fig. 2.1.
• Add paper clips to one of the mass hangers until the mass hangers start to move.
• Record the number $p$ of paper clips added to the mass hanger.
p = ...............................................................[1]
(ii) • Remove the paper clips from the mass hanger.
• Add paper clips to the other mass hanger until the mass hangers start to move.
• Record the number $q$ of paper clips added to the mass hanger.
q = ...............................................................
• Calculate $\frac{(p + q)}{2}$
\(\frac{(p + q)}{2} = .................................................................\)
[1]
(c) Using the thinner string, repeat (a)(i), (a)(iii) and (b).
d = ............................................................... mm
A = ...............................................................
p = ...............................................................
q = ...............................................................
\(\frac{(p + q)}{2} = ...............................................................\)
[3]
(d) It is suggested that the relationship between $p$, $q$ and $A$ is
\(\left [ \frac{(p + q)}{2} \right ]^3 = kA\)
where $k$ is a constant.
(i) Using your data, calculate two values of $k$.
first value of $k$ = ...............................................................
second value of $k$ = ...............................................................
[1]
(ii) Explain whether your results support the suggested relationship.
.............................................................................................
.............................................................................................
.............................................................................................
.............................................................................................[1]
(e) (i) Describe four sources of uncertainty or limitations of the procedure for this experiment.
1. .............................................................................................
.............................................................................................
2. .............................................................................................
.............................................................................................
3. .............................................................................................
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4. .............................................................................................
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[4]
(ii) Describe four improvements that could be made to this experiment. You may suggest the use of other apparatus or different procedures.
1. .............................................................................................
.............................................................................................
2. .............................................................................................
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3. .............................................................................................
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4. .............................................................................................
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[4]
512
527
600
