Use of Measuring Instruments & Electrical Equipment (OCR A Level Physics): Exam Questions

A student investigates the oscillations of a mass hanging from a spring. She pulls the mass down a short distance and releases it. She uses a hand-held stopwatch to measure the time for 10 complete oscillations.

She repeats the timing three times. Her results are shown in Table 1.1.

Table 1.1

Calculate the mean period T of the oscillations.

T = .................................................. s

The student estimates that the uncertainty in each timing in Table 1.1 is ± 0.2 s.

Calculate the percentage uncertainty in T.

percentage uncertainty = .................................................. %

Explain why timing 10 oscillations, rather than one oscillation, gives a smaller percentage uncertainty in T.

A student investigates the frictional force between a wooden block and a sloping board. One end of the board rests on a support so that the board slopes at a fixed angle.

The student attaches an analogue newton-meter to the block. She always holds the newton-meter parallel to the board.

State one safety precaution the student should take during this experiment.

The student pulls the block up the board at a steady speed. The newton-meter reads $4.5\text{ N}$.

She then lets the block slide down the board at a steady speed, holding it back with the newton-meter. The newton-meter now reads $1.1\text{ N}$.

The frictional force on the block has the same size in both cases.

Determine the frictional force F on the block.

F = .................................................. N

The student repeats the measurement of the pull needed to move the block up the board at a steady speed. Her three readings are $4.5\text{ N}$, $4.8\text{ N}$ and $4.3\text{ N}$.

Explain why the readings differ, and suggest how the student could obtain a more reliable value for the pull.

A student determines the density of the metal of a solid cylinder.

She measures the length L of the cylinder with a pair of vernier calipers. Fig. 1.1 shows the scales of the calipers when the jaws are closed, with nothing between them.

Fig. 1.1

(i) State the zero error of the calipers.

zero error = .................................................. mm

[1]

(ii) Fig. 1.2 shows the scales when the cylinder is held between the jaws.

Fig. 1.2

Determine the length L of the cylinder.

L = .................................................. mm

[2]

The diameter d of the cylinder is 12.00 mm. The mass m of the cylinder, measured with a top-pan balance, is 33.5 g.

Calculate the density ρ of the metal.

ρ = .................................................. kg m^-3

Another student measures the same cylinder with the same calipers, but she forgets to correct her reading for the zero error. She uses the same values of d and m.

Explain how this affects her value of the density ρ.

A student investigates the speed v of sound in air.

A loudspeaker connected to a signal generator emits short pulses of sound. Two microphones, M1 and M2, are placed in a straight line with the loudspeaker, with M1 nearer to the loudspeaker. The distance between the microphones is d.

Each microphone is connected to one input of a dual-trace oscilloscope. Both traces use the same time-base setting, so the time t between the start of the pulse at M1 and the start of the pulse at M2 can be measured.

Fig. 1.1 shows the two traces when $d=0.50\text{ m}$. The time-base is set to $0.5{\text{ ms div}}^{-1}$.

Fig. 1.1

(i) Determine the time t.

t = .................................................. ms

[1]

(ii) The student can locate the start of each pulse to within ± 0.1 division.

Show that the percentage uncertainty in t is about 6 %.

[2]

The student varies d and measures t for each value of d. The time-base is kept at $0.5{\text{ ms div}}^{-1}$. Each value of t is the mean of several repeat readings. The results are shown in Table 1.1.

Table 1.1

(i) Use the data in Table 1.1 to determine the speed v of sound in air.

v = .................................................. m s^-1

[3]

(ii) The student's teacher says that the data in Table 1.1 show a systematic error.

Explain how the data show this, and suggest one possible cause of the systematic error.

[2]

Another student suggests that the time-base should be changed to $0.2{\text{ ms div}}^{-1}$ for every reading in Table 1.1, to reduce the percentage uncertainty in each value of t.

The oscilloscope screen is 10 divisions wide, and the pulse at M1 always starts 1.0 division from the left-hand edge of the screen.

Evaluate this suggestion.

A student is given a sealed box with two terminals. The box contains one component, which is a fixed resistor, a filament lamp or a semiconductor diode.

The student first sets up the circuit shown in Fig. 1.1.

Fig. 1.1

The power supply has an e.m.f. of $6.0\text{ V}$ and negligible internal resistance. The ammeter has negligible resistance. The variable resistor can be set to any resistance from zero to $30\text{ Ω}$.

(i) To check the circuit, the student connects a resistor of resistance $20\text{ Ω}$ in place of the box.

Calculate the smallest potential difference (p.d.) that can be obtained across the $20\text{ Ω}$ resistor with this circuit.

p.d. = .................................................. V

[2]

(ii) The variable resistor has three terminals: one at each end of its resistance track and one on a sliding contact that can be moved along the track.

The student wants to vary the p.d. across the box from zero up to $6.0\text{ V}$.

Draw a circuit diagram, using the same apparatus, that allows the student to do this.

[2]

Describe how the student should use the circuit from (a)(ii) to obtain a set of results, and explain how the results would show which component is in the box.

A student determines the acceleration of free fall g.

A steel ball is held by an electromagnet above two light gates, A and B, as shown in Fig. 1.1. Light gate B is directly below light gate A. When the electromagnet is switched off, the ball falls from rest through the light beam of gate A and then through the light beam of gate B.

Fig. 1.1

Both light gates are connected to a data logger. The data logger records the time for which the ball blocks each light beam, to the nearest 0.01 ms. The student measures the diameter d of the ball with a micrometer.

The student's measurements are shown in Table 1.1.

Table 1.1

Explain why the student uses light gates and a data logger, rather than a stopwatch, to measure t_A and t_B. A typical human reaction time is about 0.2 s.

Use the data in Table 1.1 to determine a value for g.

g = .................................................. m s^-2

The accepted value of g is $9.81{\text{ m s}}^{-2}$. The student estimates that the uncertainty in her value of g is $\pm 0.1{\text{ m s}}^{-2}$.

Explain what this shows about the errors in the student's experiment.

The student's value of g is greater than the accepted value.

(i) The student suggests that air resistance on the ball caused the difference between her value and the accepted value.

Evaluate this suggestion.

[2]

(ii) Suggest one other possible cause of the difference, and explain how it makes her value of g too large.

[2]