No questions found
In this experiment, you will investigate the motion of a ball and rod.
(a) Press the ball of modelling clay onto the end of the wooden rod, as shown in Fig. 1.1.
(b) (i) Set up the apparatus as shown in Fig. 1.2 with the nail through the hook in the wooden rod.
(ii) Measure and record the distance $L$ between the nail and the centre of the ball.
$L =$ .............................................................
(c) Move the bottom of the rod to the left.
Release the rod and watch the movement.
The rod will move to the right and then to the left again, completing a swing as shown in Fig. 1.3.
Measure and record the time for at least 10 swings.
Record enough readings to determine an accurate value for the time $T$ taken for one complete swing.
$T =$ ......................................................... [2]
(d) Decrease $L$ by moving the ball along the rod, and repeat (b)(ii) and (c) until you have six sets of values of $L$ and $T$.
Include values of $T^2L$ and $L^2$ in your table.
[10]
(e) (i) Plot a graph of $T^2L$ on the $y$-axis against $L^2$ on the $x$-axis.
[3]
(ii) Draw the straight line of best fit.
[1]
(iii) Determine the gradient and $y$-intercept of this line.
$ ext{gradient} =$ .................................................
$y$-intercept $=$ ............................................. [2]
(f) The quantities $T$ and $L$ are related by the equation
$$T^2L = AL^2 + B$$
where $A$ and $B$ are constants.
Use your answers in (e)(iii) to determine the values of $A$ and $B$.
Give appropriate units.
$A =$ ........................................................
$B =$ ........................................................ [2]
549
544
515
(a) (i) You have been provided with a ball and a board.
Place the board on the bench.
Hold the ball above the board as shown in Fig. 2.1.
Move the ball until the height $h_1$ of the bottom of the ball above the board is 40 cm.
(ii) Release the ball.
Measure and record the maximum height $h_2$ of the ball after rebound.
\( h_2 = \text{..............................................}[2] \)
(iii) Calculate $q$, where
\( q = \frac{h_2}{h_1} \).
\( q = \text{.................................................} \)
(b) (i) Raise the board so that it makes an angle $\theta$ with the bench as shown in Fig. 2.2.
(ii) Adjust the board until $\theta$ is in the range 10° to 12°.
Measure and record $\theta$.
\( \theta = \text{................................................}[1] \)
(iii) Calculate $\cos^2(2\theta)$.
[\( \cos^2(2\theta) = \cos(2\theta) \times \cos(2\theta) \)]
\( \cos^2(2\theta) = \text{..............................................}[1] \)
(iv) Justify the number of significant figures that you have given for your value of \( \cos^2(2\theta) \).
......................................................................................................
......................................................................................................
......................................................................................................
...................................................................................................... [1]
(c) (i) Place the large container on its side with its open face towards the board as shown in Fig. 2.3.
(ii) Hold the ball 40 cm above the board.
(iii) Release the ball. Watch it bounce at A and follow a curved path before bouncing into the container.
Measure and record the maximum height $h$ of the ball after rebound, as shown in Fig. 2.3.
\( h = \text{......................................................}[1] \)
(iv) Estimate the percentage uncertainty in your value of $h$.
percentage uncertainty = \text{......................................................}[1]
(d) (i) Adjust the board until $\theta$ is in the range 20° to 22°.
Measure and record $\theta$.
\( \theta = \text{..................................................}[1] \)
(ii) Repeat (b)(iii), (c)(ii) and (c)(iii).
\( \cos^2(2\theta) = \text{...............................................} \)
\( h = \text{................................................}[2] \)
(e) It is suggested that the relationship between $h$, $q$ and $\theta$ is
\( h = kq \cos^2 (2\theta) \)
where $k$ is a constant.
(i) Using your data, calculate two values of $k$.
first value of $k = \text{...................................................}$
second value of $k = \text{..................................................}$ [1]
(ii) Explain whether your results support the suggested relationship.
......................................................................................................
......................................................................................................
......................................................................................................
...................................................................................................... [1]
(f) (i) Describe four sources of uncertainty or limitations of the procedure for this experiment.
1. .............................................................................................................................
...........................................................................................................................
2. .............................................................................................................................
...........................................................................................................................
3. .............................................................................................................................
...........................................................................................................................
4. .............................................................................................................................
........................................................................................................................... [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. .............................................................................................................................
...........................................................................................................................
3. .............................................................................................................................
...........................................................................................................................
4. .............................................................................................................................
........................................................................................................................... [4]
502
532
570
