Manipulation, Measurement and Observation

Pass the string through the shorter tube, as shown in Fig. 2.1a. Pass one loop through the other loop, as shown in Fig. 2.1b, to secure the tube in place, as shown in Fig. 2.1c.

Hang the string from the clamp, as shown in Fig. 2.2.

Displace the tube, as shown in Fig. 2.3. Release the tube.

The time the tube takes to return to the release position for the first time is the time period $T$. This may be determined accurately by measuring the time taken for the tube to complete several swings, backwards and forwards.

Showing all your working, determine an accurate value for the time period $T$.

$T$ = ______ $\text{s}$

Using the vernier calipers, measure the length $l$ of the shorter tube, as shown in Fig. 2.3.

$l$ = ______

Explain how you have made this measurement as accurate as possible.

Pass the string through the longer tube so that it rests above the shorter tube, as shown in Fig. 2.4.

Repeat (b) to determine the new value of $T$.

new value of $T$ = ______

Measure the length of the longer tube.

length of the longer tube = ______

• Connect the circuit shown in Fig. 1.1.

• Ensure that the switch S is open.

• Slide the LDR leads into the tube until the front of the LDR is just level with the open end of the tube, as shown in Fig. 1.1.

• With the LDR in this position, attach a piece of adhesive tape to the leads as a marker at the other end of the tube, as shown in Fig. 1.1.

• Slide the tube until the LDR is approximately half-way along it, as shown in Fig. 1.2.

• The distance between the tape and the tube is $x$.

Measure and record $x$.

$x$ = ______

• Close S and record the ammeter reading $I$.

$I$ = ______

• Open S.

Change $x$ by moving the LDR to a new position inside the tube, with $x$ in the range $4\ \text{cm}$ to $18\ \text{cm}$. Record $x$ and $I$.

Repeat until you have six sets of values of $x$ and $I$.

Record your results in a table. Include values of $\sqrt{I}$ in your table.

• Draw a straight line of approximate length $20\text{ cm}$ on the sheet of paper.
• Mark point X at the centre of this line as shown in Fig. 1.1.

• Rotate the paper so that the straight line on the paper is aligned with the N–S direction shown by the plotting compass, as shown in Fig. 1.2.
Keep the magnets away from the plotting compass while you are doing this.

• Fix the paper to the bench in this position using adhesive putty.
The paper should stay in this position throughout the experiment.
• Set up the apparatus as shown in Fig. 1.3.

• Adjust the position of the stand until the small magnet is directly over point X on the paper.
• The distance between the bottom of the small magnet and the paper is $h$.
Adjust the height of the boss until $h$ is $3.0\text{ cm}$.
• Displace the small magnet through a short distance in the direction of the line on the paper.
• Release the small magnet. The small magnet will oscillate.
• The period of the oscillations of the small magnet is $T_0$.
Take measurements to determine $T_0$.

$T_0$ = ______

• Place the bar magnet on the sheet of paper at the position shown in Fig. 1.4.

• Draw around the bar magnet. Do not move it from this position.
• Displace the small magnet through a short distance in the direction of the line on the paper. Release the small magnet. The small magnet will oscillate.
• The period of the oscillations of the small magnet is $T$.
Record $h$ and determine $T$.

$h$ = ______
$T$ = ______

Write down your value of $T_0$ from (a).

$T_0$ = ______

Change the height of the boss such that $h$ is in the range $3.0\text{ cm} \leq h \leq 9.0\text{ cm}$.
For each value of $h$, determine $T$.
Repeat until you have six sets of values of $h$ and $T$. Include your values from (b).
Record your results in a table. Include values of $\frac{T}{T_0}$ in your table.

• Slide the double spring and the two single springs onto the longer wooden rod.
• Set up the apparatus as shown in Fig. 1.1.

• Use the bosses to fix the wooden rod approximately $55\text{ cm}$ above the bench and parallel to the bench.
• Hang a total mass of $270\text{ g}$ from the double spring.
• The mass hanging from the double spring is $m$.

Record $m$.

$m$ = ______

• Gently pull the mass down through a short distance. When released, the mass will oscillate.
• Take measurements to determine the period $T_1$ of the oscillations.

$T_1$ = ______

• Remove the mass from the double spring.

• Using the shorter wooden rod, hang mass $m$ as shown in Fig. 1.2.

• Gently place the hook of the mass hanger near the centre of the shorter rod.
• Carefully adjust the position of the mass hanger until the shorter rod is approximately parallel to the bench, as shown in Fig. 1.2.
• Gently pull the mass down through a short distance. When released, the mass will oscillate.
• Take measurements to determine the period $T_2$ of the oscillations.

$T_2$ = ______

• Remove the mass.

Vary $m$. For each value of $m$, determine $T_1$ and $T_2$. Repeat until you have five sets of values of $m$, $T_1$ and $T_2$. Do not use values of $m$ less than $200\text{ g}$.

Record your results in a table. Include values of $\sqrt{T_1}$ and $\sqrt{T_2}$ in your table.

• Assemble the apparatus as shown in Fig. 1.1.

• Mass A and mass B are each $200\text{ g}$.
• Add a mass $z$ of $40\text{ g}$ to mass B.
Record the value of $z$.

$z$ = ______ $\text{g}$

• $M$ is given by $M = 200\text{ g} + z$.
Calculate $M$.

$M$ = ______ $\text{g}$

• Pull both A and B down a short distance and release them together. Observe the oscillations. A and B initially oscillate in phase (both moving up and down together), then their oscillations go out of phase and then become in phase again.
• The time from A and B oscillating in phase to the next time they oscillate in phase is $P$.
Measure and record $P$.

$P$ = ______

Change $z$ and determine $P$. Repeat until you have six sets of values of $z$ and $P$.
Record your results in a table. Include values of $M$, $\frac{1}{\sqrt{M}}$ and $\frac{1}{P}$ in your table.

• Assemble the apparatus as shown in Fig. 1.1.

• Mass A and mass B are each $200\text{ g}$.
• Add a mass $z$ of $40\text{ g}$ to mass B.

Record the value of $z$.

$z$ = ______ $\text{g}$

• $M$ is given by $M = 200\text{ g} + z$.

Calculate $M$.

$M$ = ______ $\text{g}$

• Pull both A and B down a short distance and release them together. Observe the oscillations. A and B initially oscillate in phase (both moving up and down together), then their oscillations go out of phase and then become in phase again.
• The time from A and B oscillating in phase to the next time they oscillate in phase is $P$.

Measure and record $P$.

$P$ = ______

Change $z$ and determine $P$. Repeat until you have six sets of values of $z$ and $P$.

Record your results in a table. Include values of $M$, $\frac{1}{\sqrt{M}}$ and $\frac{1}{P}$ in your table.

• Assemble the apparatus as shown in Fig. 1.1 and Fig. 1.2.
• Push the nail through the central hole in the pendulum and then into the plastic tube.
• Secure the tube and nail in the boss, as shown in Fig. 1.1.

• Ensure that the pendulum swings freely on the nail.

• Attach two 50g slotted masses to the pendulum using the bolts and nuts. Use two holes which are the same distance $x$ from the nail, as shown in Fig. 1.3.

• The distance from the centre of each bolt to the nail is $x$.
• Measure and record $x$.

$x$ = ______

Push the bottom of the pendulum a short distance to one side and then release it.
Take measurements to determine the period $T$ of the oscillations.

$T$ = ______

Vary $x$ by using different holes and measure $T$.

Repeat until you have six sets of values of $x$ and $T$.

Record your results in a table. Include values of $\sqrt{x^3}$ in your table.

● Connect the circuit shown in Fig. 1.1.

● Ensure that the polarities of the power supply, component C and the voltmeter are as shown in Fig. 1.1.

● Close switch S for a short time and then open it.

● Watch the voltmeter reading as it reduces.

When the voltmeter reading passes a value $V_S$ of $8.00\text{ V}$, start the stop-watch.

When the voltmeter reading passes a value of $7.00\text{ V}$, stop the stop-watch.

● Record the starting value $V_S$ and the time $T$ for the voltmeter reading to fall by $1.00\text{ V}$.

$V_S$ = ______
$T$ = ______

Choose another starting value $V_S$. Close S for a short time and then open it. Measure the time $T$ for the voltmeter reading to fall by $1.00\text{ V}$ from the starting value $V_S$.

Repeat until you have six sets of values of $V_S$ and $T$.

Record your results in a table. Include values of $\frac{1}{T}$ in your table.

● Set up the apparatus as shown in Fig. 1.1.

● Place the slotted mass in the string loop attached to the springs.
● Pull the slotted mass downwards through a small distance.
● Release the mass. The mass will oscillate.
● Determine the period $T_0$ of the oscillations of the mass.

$T_0$ = ______

● Remove the slotted mass from the string loop attached to the springs.

● Set up the apparatus as shown in Fig. 1.2.

● Position the string loop attached to the springs at the 50 cm mark on the rule. This string loop must remain in this position throughout the experiment.
● The distance between the string loop supporting the slotted mass and the end B of the rule is $x$.

Position the mass so that $x$ is approximately 20 cm.

● Adjust the apparatus so that the rule is parallel to the bench and the springs are vertical.
● Record $x$.

$x$ = ______

● Pull B downwards through a small distance.
● Release B. The rule will oscillate.
● Determine the period $T$ of the oscillations of the rule.

$T$ = ______

Change $x$ by moving the mass along the rule. For each value of $x$, adjust the apparatus so that the rule is parallel to the bench and the springs are vertical, then determine $T$.

Repeat until you have six sets of values of $x$ and $T$ with $x$ in the range $10\ \text{cm} \leq x \leq 40\ \text{cm}$.

Record your results in a table. Include values of $(T - T_0)^2$ in your table.

• Set up the apparatus as shown in Fig. 1.1.

• Ensure the rod of the clamp is approximately $15\text{ cm}$ above the bench.
• Arrange the wooden strip so that the bottom of the strip rests against the base of the stand.
• Use adhesive putty to fix the string centrally on the wooden strip in line with the spring.
• Wrap the string around the screw.

• Arrange the block and protractor as shown in Fig. 1.2.

• The length of the coiled section of the spring is $L_0$, as shown in Fig. 1.2.

The angle between the lower edge of the wooden strip and the horizontal is $\theta_0$, as shown in Fig. 1.2.

Adjust the apparatus until $\theta_0$ is between $75^\circ$ and $85^\circ$. You may wish to move the protractor along the block.

• Measure and record $L_0$ and $\theta_0$.

$L_0$ = ______
$\theta_0$ = ______ $^\circ$

• Make a hook from one paper clip and hang nine paper clips from it as shown in Fig. 1.3.

• The mass of all ten paper clips is $m$.

Measure and record $m$.

$m$ = ______

• Using the mass hanger and slotted masses, hang a mass of $40\text{ g}$ from the string loop.

• Hang the paper clips from the string loop as shown in Fig. 1.4.

• The total mass hanging from the string loop is $M$.

The angle between the wooden strip and the horizontal is $\theta$, as shown in Fig. 1.4.

The length of the coiled section of the spring is $L$, as shown in Fig. 1.4.

Determine and record $M$.

$M$ = ______

• Measure and record $\theta$ and $L$.

$\theta$ = ______ $^\circ$
$L$ = ______

• Calculate $e$ where

$e$ = ______

Vary $M$. The total mass $M$ may be made from slotted masses only or from $m$ and slotted masses. For each value of $M$, measure and record $M$, $\theta$ and $L$. Repeat until you have six sets of values.

Record your results in a table. Include values of $e$ and $\sin\theta$ in your table.