ATP- REVISION

1- A voltmeter is specified as being accurate within 2%. The reading on the voltmeter is 3.50V. The difference between maximum and minimum voltage represented by these reading is

a. 0.14Vb. 0.07Vc. 3.57Vd. 3.43V

2- A student checks the diameter of a ball bearing and records the following values. 5.1 mm, 5.0mm, 5.0mm.The average value should be recorded as

a. 5.0mmb. 5.033mmc. 5.03mmd. 5.1mm

3- The depression x at the centre of a rule supported symmetrically between 2 knife edges is given by the expression, ϰ = Mgl3 / 4Ebd3. If M,g,E are constants, the % uncertainty of x can be calculated as

a. % M + % g + 3% l + % E + % b + 3% db. 3% l + % b + 3% dc. % l + % b + % dd. 3% l + % g + 3% d + %b

4- A simple pendulum arrangement is used to find a value for acceleration of free fall. The value is found to be 10.8ms-2. The % difference between this and actual value is

a. 10.1%b. 9.17% c. 9.61%d. 0.0917%

5- The absolute uncertainty of micrometer screw gauge is,a. 0.01cmb. 0.1cmc. 0.01mmd. 0.1mm

6- A marble rolls down an inclined plane. The average time taken to cover the distance ϰ= 1m, is 2.30s. Distance is measured using meter ruler. Acceleration is given by, a= 2ϰ/t2. What is % uncertainty of a?

a. 8.8%b. 10.8% c. 9.7% d. 1.86%

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7- A trolley with an interrupter card of length 20cm cuts the light gate as shown.Time to cut top gate = 0.3 sTime to cut bottom gate = 0.14 sTime to travel between the gates = 0.50 sWhat is the acceleration of the trolley?

a. 1.52ms-2

b. 4.2ms-2

c. 3.45ms-2

d. 1.72ms-2

8- All the springs in the diagram are identical. A 4kg mass produces an extension of 3cm on A. What will be the extension produced by the combination (ii) and (iii) ?

9- A student performing an experiment with a vibrating wire. The length l of vibrating part of the wire is 72.2cm (meter ruler). The diameter of the wire is 0.23mm (screw gauge).

a. Estimate the % uncertainty in the value of l and d.b. Calculate the value for the density of the material from which the

wire is made, given that ρ = T / πd2f2l2 , f = 50Hz, T = 1.96Nc. Determine the % uncertainty in density?d. The accepted value for the density of constantan is 8880kgm-3.

Discuss whether the wire used could be made from constantan?

10 A student is taking measurements from a piece of wire. (a) She measures the diameter d using a micrometer. She obtains the following readings. d/mm 0.27, 0.29, 0.26, 0.77, 0.26 (i) Explain how you would use her readings to obtain the most accurate mean value

for the diameter of the wire.

(ii) Use her readings to obtain the most accurate mean value for the diameter of the

wire. (iii) Estimate the percentage uncertainty in your value for the diameter

of the wire.

(b) She then makes the following measurements. length of wire = 663 mm

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mass of wire = 0.32 g (i) Use her measurements to calculate the volume of the wire. (ii) Calculate the density of the material of the wire.

(c) The tables below are taken from a data book. Use the information in the tables to identify the material of the wire and its standard thickness.

Material of wire is -------- Standard thickness of wire is ----------------

15 A student is investigating kinetic energy. He sets up the apparatus as shown.

The trolley starts from rest with the weight close to the pulley and at a height h above the floor. (a) Describe how you would measure the height h. You may add to the diagram if you wish. (b) The student records the distance h and the time t it takes for the weight to fall to the floor. His measurements are shown below. h = 885 mm t/s 2.94 2.76 3.28 3.15 3.02 The maximum velocity of the trolley is given by 2h/t (i) Estimate the uncertainty in the value for h. This should relate to your method in part (a). (ii) Estimate the uncertainty in the readings for t. (iii) Calculate the mean maximum velocity.

(iv) The mass of the trolley is 0.930 kg and the falling weight has a mass of 0.030 kg. Calculate a value for the total maximum kinetic energy of the trolley and weight.

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(v) Estimate the percentage uncertainty in your calculated value for the kinetic energy. Assume the uncertainty in the values of both masses is negligible.

16 In 2006 astronomers determined a new value for the Hubble constant. They calculated velocity of recession v for a number of stars at a distance d from the Earth. They used units of km s–1 for v and Mpc (Megaparsecs) for d.

a The graph below is a plot of their data.

(i) Draw a line of best fit for this data.

(ii) Determine the gradient of your

line.

b (i) Hubble’s law states that v is directly proportional to d. Explain whether the plotted data supports Hubble’s law.

(ii) The value of the gradient is the Hubble constant. Until 2006, the accepted value of the Hubble constant was 71 km s–1 Mpc–1. Calculate the percentage difference between this accepted value and your value.

17 For gamma rays passing through lead of thickness x, the count rate A is given by A = A0 e-µx

where A0 is the count rate when there is no lead between source and detector, and μ is a constant. a Explain why a graph of ln A against x should be a straight line.

b The following data were obtained in such an investigation.

Use the column(s) provided for your processed data, and then plot a suitable Grade 12 Page 4

graph on the grid opposite to show that these data are consistent with A = A0 e-

µx.

C Use your graph to determine a value for the constant μ.

18 A student investigates skateboarding down a slope. She times how long it takes her to skateboard between two lines on a sloping pavement. She varies the distance between the two lines and records her results in a table.

The student read that the equation which might relate to the motion of the skateboard iss = ut + (½) at2

a Criticise her set of measurements.

b Plot a graph of s/t against t. Use the extra column in the table for your values of s/t.

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(c) Use the equation to show that this graph should produce a straight line.

(d) Use your graph to calculate a and u.

18 The force F acting on a length l of wire carrying a current I in a magnetic field of flux density B is given by F = BIlsinθ The diagram shows an arrangement for investigating this relationship. For clarity, theclamps supporting the rigid wire have been omitted.

(a) Add to the diagram to show (i) precisely the length l that you would need to measure (ii) that the angle θ is 90° in this arrangement.(b) State what measurements you would need to take to determine the force F acting on the wire when there is a current I in the wire, and how you would use these measurements to calculate F.(c) The table shows data obtained from this arrangement. I / A 1.0 1.5 2.0 2.5 3.0 3.5 F/ mN 18.6 27.3 35.7 44.1 52.3 60.5Grade 12 Page 6

(i) Plot a graph of F against I on the grid below. (ii) Discuss the extent to which your graph confirms that F α I.19 A student is asked to determine the acceleration of free fall, g, by timing the swings of a Mass hanging on the end of a string. The equation she is given is T= 2π√¿¿) , where T is the period taken for the mass to

Make one complete swing from A to B and back to A, and l is the length of the string.

a) Her results are shown in the table below.

Criticize this set of measurements.(b) Plot a graph of T2 against l. Use the extra column in the table for your values of T2.

(c) Use the equation to show why the graph is a straight line.

(d) Use your graph to determine a value for g.

(e) The accepted value for g is 9.81 m s-2. Calculate the percentage difference between the value you have determined and the accepted value.

20 for a hot object cooling in a draught, the excess temperatures θ recorded at times t were as follows

t/min 0 5 10 15 20 25 30

θ/0c 60 50 40.5 31.5 25.8 20.1 16.5

Show that the results agree with,

θ = θ0 e-At and deduce the values of the constants A and θ0

21 The activity A of a radioactive sample decreases with time t giving the following results

t/day 0 20 40 60 80 100

A/Bq 1000 830 665 545 446 368

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If A = A0 e-λt , where A0 and λ are constants. Plot a suitable straight line graph and from it determine λ

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