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In this experiment, you will investigate the extension of one of the springs supporting a load as the load is varied.
The apparatus has been partly assembled.
Complete the assembly by suspending the mass hanger (with no masses on it) from the central loop, as shown in Fig. 1.1.
Note that two marks 0.100 m apart have been made on the string.
(a) Record the suspended mass $M$ (the mass of the mass hanger).
(b) (i) Measure the length $l$ of the coiled section of spring A, as shown in Fig. 1.1.
(ii) Hence calculate the extension $x$ of the spring (the unloaded length is written on a card).
(c) Measure the heights of the marks above the bench and use these to find the vertical separation $v$ of the marks (see Fig. 1.1).
Show your working.
(d) Add more mass to the hanger and repeat (a), (b) and (c) until you have six sets of readings for $M$, $l$, $x$ and $v$.
Include values of $\frac{M}{v}$ in your table.
(e) (i) Plot a graph of $\frac{M}{v}$ on the $y$-axis against $x$ on the $x$-axis.
(ii) Draw the line of best fit.
(iii) Determine the gradient and $y$-intercept of the line of best fit.
(f) The quantities $M$, $v$ and $x$ are related by the equation
$$\frac{M}{v} = qkx + qC$$
where $q$ is a constant, $k$ is the spring constant (the value of $k$ is written on a card) and $C$ is the tension required for the initial separation of the spring's coils.
Using your answers from (e)(iii), determine the value of $C$.
565
515
580
In this experiment, you will investigate how the frictional force between a wooden rod and nylon thread varies with the length of thread in contact with the rod.
(a) Use the vernier calipers to determine the diameter $d$ of the wooden rod.
Show all your working.
(b) Estimate the percentage uncertainty in $d$.
(c) Assemble the apparatus as shown in Fig. 2.1.
The 10 g mass is already attached to one end of the thread. Attach the 50 g mass hanger to the other end.
The thread is wrapped 1.5 times around the rod. The turns of thread must not touch each other.
(d) Use your value from (a) to calculate the length $l$ of thread in contact with the rod. (Circumference of rod = \(\pi d\)).
Show all your working.
(e) Add masses to the hanger until the hanger just starts to move down to the bench.
Record this mass $m$ (including the mass of the hanger).
(f) Remove the masses from the hanger and then wrap the thread one more time around the rod, so that it is now wrapped around the rod 2.5 times.
Repeat steps (d) and (e).
(g) It is suggested that $m$ and $l$ are related by the equation
$$m^2 = kl^3$$
where $k$ is a constant.
By calculating values of $k$, explain whether your results support this relationship.
(h) (i) State and explain four sources of error or limitations of the procedure in this experiment.
(ii) Suggest and explain four improvements that could be made to this experiment. You may suggest the use of other apparatus or different procedures.
515
536
545
