Planning

Fig. 1.1 shows two identical cylindrical metal conductors P and Q, each of length $L$ and cross-sectional area $A$.

The conductors are placed parallel to each other. The perpendicular distance from the midpoint of P to point X is $p$. The perpendicular distance from the midpoint of Q to point X is $q$.

The two conductors are electrically connected in parallel. This parallel combination is connected in series to a power supply and a resistor. The potential difference $V$ between the ends of P is the same as the potential difference between the ends of Q.

The magnetic flux density at X due to the currents in the conductors is $B$.

It is suggested that $B$ is related to $p$ by the relationship

$$B = \frac{YAV}{Lp} + \frac{YZAV}{Lq}$$

where $Y$ and $Z$ are constants.

Plan a laboratory experiment to test the relationship between $B$ and $p$.

Draw a diagram showing the arrangement of your equipment.

Explain how the results could be used to determine values for $Y$ and $Z$.

In your plan you should include:

• the procedure to be followed
• the measurements to be taken
• the control of variables
• the analysis of the data
• any safety precautions to be taken.

Fig. 1.1 shows a thin coil of cross-sectional area $A$ and length $l$ connected to a resistor of resistance $S$ and two terminals.

An alternating voltage is applied to the terminals. The peak value of the alternating voltage is $E$ and the frequency is $f$. The peak value of the potential difference $V$ across the resistor is determined using an oscilloscope.

It is suggested that $V$ is related to $f$ by the relationship

$$\frac{ES}{V} = \frac{KAN^2f}{l}$$

where $N$ is the number of turns on the coil and $K$ is a constant.

Plan a laboratory experiment to test the relationship between $V$ and $f$.

Draw a diagram showing the arrangement of your equipment.

Explain how the results could be used to determine a value for $K$.

In your plan you should include:

• the procedure to be followed
• the measurements to be taken
• the control of variables
• the analysis of the data
• any safety precautions to be taken.

A thin solid disc of radius $r$ and thickness $z$ is attached to a thin axle. String is wrapped around the axle, as shown in Fig. 1.1.

A block of mass $m$ is attached to the string.

The block is released from rest and falls downwards. The block has speed $v$ when it has fallen through a distance $h$ from the point of release. The value of $v$ is determined using one light gate connected to a timer.

It is suggested that $v$ is related to $m$ by the relationship

$$\frac{h}{v^2} = \frac{\pi r^2 z}{2PQm} + \frac{1}{P}$$

where $P$ and $Q$ are constants.

Plan a laboratory experiment to test the relationship between $v$ and $m$.

Draw a diagram showing the arrangement of your equipment.

Explain how the results could be used to determine values for $P$ and $Q$.

In your plan you should include:

• the procedure to be followed
• the measurements to be taken
• the control of variables
• the analysis of the data
• any safety precautions to be taken.

Fig. 1.1 shows a thin coil of cross-sectional area $A$ and length $l$ connected to a resistor of resistance $S$ and two terminals.

An alternating voltage is applied to the terminals. The peak value of the alternating voltage is $E$ and the frequency is $f$. The peak value of the potential difference $V$ across the resistor is determined using an oscilloscope.

It is suggested that $V$ is related to $f$ by the relationship

$$\frac{ES}{V} = \frac{KAN^2f}{l}$$

where $N$ is the number of turns on the coil and $K$ is a constant.

Plan a laboratory experiment to test the relationship between $V$ and $f$.

Draw a diagram showing the arrangement of your equipment.

Explain how the results could be used to determine a value for $K$.

In your plan you should include:

• the procedure to be followed
• the measurements to be taken
• the control of variables
• the analysis of the data
• any safety precautions to be taken.

A ball is dropped on to an inclined thin metal sheet, as shown in Fig. 1.1.

The angle between the sheet and the horizontal bench is $\theta$. The height of the point of contact of the ball and the sheet is $z$. The horizontal distance travelled by the ball between its points of contact with the sheet and the bench is $d$, as shown in Fig. 1.1.

It is suggested that $d$ is related to $\theta$ by the relationship

$$d = \frac{Pv^2 \sin 4\theta}{g} + Q\sqrt{z}$$

where $v$ is the speed of the ball as it makes contact with the sheet, $g$ is the acceleration of free fall, and $P$ and $Q$ are constants.

Plan a laboratory experiment to test the relationship between $d$ and $\theta$.

Draw a diagram showing the arrangement of your equipment.

Explain how the results could be used to determine values for $P$ and $Q$.

In your plan you should include:

• the procedure to be followed
• the measurements to be taken
• the control of variables
• the analysis of the data
• any safety precautions to be taken.

Diagram

On a bench, a steel ball of radius $r$ is used to compress a spring by a distance $x$. The ball is held at rest in this position, as shown in Fig. 1.1.

The ball is released and rolls along the bench. At a fixed point P, the ball has speed $v$. The speed of the ball at P is determined using one light gate connected to a timer.

Several steel balls of different radii are available.

It is suggested that $v$ is related to $r$ by the relationship

$$v^2 = \frac{Ykx^2}{r^n\rho}$$

where $k$ is the spring constant of the spring, $\rho$ is the density of the steel, and $Y$ and $n$ are constants.

Plan a laboratory experiment to test the relationship between $v$ and $r$.

Draw a diagram showing the arrangement of your equipment.

Explain how the results could be used to determine values for $Y$ and $n$.

In your plan you should include:

• the procedure to be followed
• the measurements to be taken
• the control of variables
• the analysis of the data
• any safety precautions to be taken.

Fig. 1.1 shows a model wind turbine with blades, each of length $L$, placed in moving air.

The area of the circle swept by the blades of the turbine is $A$.

The output of the turbine has two terminals. The turbine is connected to a resistor of resistance $R$. At a speed $v$ of the moving air, the current in the resistor is $I$.

The atmospheric pressure is $P$ and the thermodynamic temperature of the air is $T$.

It is suggested that $I$ is related to $v$ by the relationship

$$\frac{I^2 R}{Q} = \frac{APv^3}{2T}$$

where $Q$ is a constant.

Plan a laboratory experiment to test the relationship between $I$ and $v$.

Draw a diagram showing the arrangement of your equipment.

Explain how the results could be used to determine a value for $Q$.

In your plan you should include:

• the procedure to be followed
• the measurements to be taken
• the control of variables
• the analysis of the data
• any safety precautions to be taken.

On a bench, a steel ball of radius $r$ is used to compress a spring by a distance $x$. The ball is held at rest in this position, as shown in Fig. 1.1.

The ball is released and rolls along the bench. At a fixed point P, the ball has speed $v$. The speed of the ball at P is determined using one light gate connected to a timer.

Several steel balls of different radii are available.

It is suggested that $v$ is related to $r$ by the relationship

$$v^2 = \frac{Ykx^2}{r^n\rho}$$

where $k$ is the spring constant of the spring, $\rho$ is the density of the steel, and $Y$ and $n$ are constants.

Plan a laboratory experiment to test the relationship between $v$ and $r$.

Draw a diagram showing the arrangement of your equipment.

Explain how the results could be used to determine values for $Y$ and $n$.

In your plan you should include:

• the procedure to be followed

• the measurements to be taken

• the control of variables

• the analysis of the data

• any safety precautions to be taken.

Fig. 1.1 shows a horizontal turntable.

Point C is at the centre of the turntable. Point P is a distance $r$ from the centre.

Fig. 1.2 shows a side view of a d.c. motor attached to the turntable with a belt.

The motor is used to rotate the turntable at frequency $f_0$. The motor is switched off and the turntable continues to rotate at frequency $f_0$.

A sphere of adhesive putty of mass $m$ is dropped onto the turntable at point P. The frequency of the turntable is now $f$.

It is suggested that $f$ is related to $m$ by the relationship

$$\frac{Kf_0}{f} = \beta K + mr^2$$

where $\beta$ and $K$ are constants.

Plan a laboratory experiment to test the relationship between $f$ and $m$.

Draw a diagram showing the arrangement of your equipment.

Explain how the results could be used to determine values for $\beta$ and $K$.

In your plan you should include:

• the procedure to be followed
• the measurements to be taken
• the control of variables
• the analysis of the data
• any safety precautions to be taken.

Fig. 1.1 shows a thin cylindrical metal rod of length $L$.

One end of the rod is hit with a hammer. A stationary sound wave is set up within the rod. The rod vibrates at its resonant frequency $f$.

A microphone placed at the other end of the rod detects the sound wave emitted from the rod. The frequency of the detected sound is also $f$.

A number of rods of different length are available.

It is suggested that $f$ is related to $L$ by the relationship

$$2fL^n = \sqrt{\frac{E}{\rho}}$$

where $\rho$ is the density of the metal, and $E$ and $n$ are constants.

Plan a laboratory experiment to test the relationship between $f$ and $L$.

Draw a diagram showing the arrangement of your equipment.

Explain how the results could be used to determine values for $E$ and $n$.

In your plan you should include:

• the procedure to be followed
• the measurements to be taken
• the control of variables
• the analysis of the data
• any safety precautions to be taken.