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In this experiment, you will investigate the motion of a bottle in water.
(a) You have been provided with a bottle with a mass attached, a measuring cylinder, a jug of water and a large cylindrical container of water.
(i) Use water from the jug and the measuring cylinder to determine the maximum volume $V_F$ of water held by the bottle. Record $V_F$. (1 ml = 1 cm$^3$)
$V_F =$ ................................. cm$^3$ [1]
(ii) Return any water to the jug. Do not change the volume of water in the large cylindrical cylinder.
(b) (i) Add volume $V$ of water to the bottle where $V$ is approximately 100 cm$^3$.
(ii) Record $V$.
$V =$ ................................... cm$^3$
(iii) Screw the cap on the bottle so that no water leaks out of the bottle when the bottle is inverted.
(c) (i) Place both rubber bands around the top of the large cylindrical container.
(ii) Gently push the bottle into the water in the large cylindrical container until the top is just on the water surface as shown in Fig. 1.1. Keep the bottle in this position using one hand.
A diagram for Fig. 1.1 is included.
(iii) Use your other hand to slide one of the rubber bands down so that it is level with the bottom of the mass.
A diagram for Fig. 1.2 is included.
(iv) Release the bottle. The bottle will move upwards and then move downwards. Place the other rubber band so that it is level with the highest position of the bottom of the mass as shown in Fig. 1.2. You should repeat this several times before you decide on the position of this rubber band.
(v) Measure and record $y$.
$y =$ .................................. cm [1]
(d) (i) Calculate $\frac{2V_F}{3}$.
$\frac{2V_F}{3} =$ .................................. cm$^3$
(ii) Increase $V$ and repeat (b)(ii), (b)(iii), (c)(ii), (c)(iv) and (c)(v) until you have six sets of values of $V$ and $y$. Do not use a value of $V$ greater than $\frac{2V_F}{3}$.
(e) (i) Plot a graph of $y$ on the $y$-axis against $V$ on the $x$-axis. [8]
(ii) Draw the straight line of best fit. [1]
(iii) Determine the gradient and $y$-intercept of this line.
gradient = ..................................................
$y$-intercept = ..................................................
(f) The quantities $y$ and $V$ are related by the equation $y = PV + Q$ where $P$ and $Q$ are constants. Using your answers in (e)(iii), determine the values of $P$ and $Q$. Give appropriate units.
$P =$ ..........................................................
$Q =$ ..........................................................
(g) (i) Use your values from (f) to calculate the value of $V$ when $y = 0$.
$V =$ .................................. cm [1]
(ii) Explain why it is impossible to repeat the experiment using the value of $V$ calculated in (g)(i).
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(a) (i) Clamp the wooden strip as shown in Fig. 2.1.
The distance $L$ that the wooden strip extends beyond the edge of the bench should be approximately 80 cm.
(ii) Measure and record $L$.
$L = \text{..............................................}$ [1]
(iii) Estimate the percentage uncertainty in your value of $L$.
percentage uncertainty = \text{..........................}[1]
(b) (i) Place the 100 g mass on the end of the wooden strip as shown in Fig. 2.2.
The vertical distance between the floor and the bottom of the end of the wooden strip is $d_1$.
(ii) Measure and record $d_1$.
$d_1 = \text{..........................................}[1]$
(iii) Remove the 100 g mass from the wooden strip.
(c) (i) Use ten 10 g masses to evenly distribute a total mass of 100 g along the length of the wooden strip.
(ii) The distance between the floor and the bottom of the end of the wooden strip is $d_2$.
Measure and record $d_2$.
$d_2 = \text{..........................................}[1]$
(iii) Calculate $(d_2 - d_1)$.
$(d_2 - d_1) = \text{.........................................}[1]$
(iv) The mass per unit length $M$ added to the wooden strip is given by
$$M = \frac{m}{L}$$
where the total added mass $m$ is 0.100 kg.
Calculate $M$.
$M = \text{.........................................}[1]$
(d) Justify the number of significant figures that you have given for your value of $M$.
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......................................................................................................................[1]
(e) Repeat (b) using the 50 g mass and repeat (c) using five 10 g masses to evenly distribute 50 g along the length of the wooden strip.
For this mass the value of $m$ is 0.050 kg.
$d_1 = \text{.........................................}$
$d_2 = \text{.........................................}$
$(d_2 - d_1) = \text{...................................}$
$M = \text{............................................}[3]$
(f) It is suggested that the relationship between $(d_2 - d_1)$ and $M$ is $$ (d_2 - d_1) = kM $$ 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.
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......................................................................................................................[1]
(g) (i) Describe four sources of uncertainty or limitations of the procedure for this experiment.
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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.
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2. ........................................................................................................................
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[4]
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