Two forces, each of magnitude F form a couple acting on the edge

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P2_(TOPIC_5)_-_FORCE_DENSITY_AND_PRESSURE.pdf - 10 5 Two forces, each of magnitude F, form a couple acting on the edge of a disc of radius r, as shown

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This page covers Questions and Worked Solutions for Physics 9702 Paper 12 October 2021, 9702/12.

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May 2021 Physics 9702 Paper 12 (pdf)

• Solutions

1. What is not a reasonable estimate of the physical property indicated?
2. Which quantity could have units of N m V–1?
3. An object is acted upon by two forces, 10 N in the vertical direction and 6 N at 40 to the vertical, as shown.
4. An analogue ammeter with a range of 0–250 mA is connected into an electrical circuit. The diagram shows the ammeter’s display.
5. Students take readings of the volume of a liquid using three different pieces of measuring equipment X, Y and Z.
6. Which graph shows the variation with time t of the velocity v of an object falling vertically downwards in a vacuum?
7. A projectile is fired from point P with velocity V at an angle  to the horizontal. It lands at point Q, a horizontal distance R from P. Air resistance is negligible
8. A book of weight W is at rest on a table. A student attempts to state Newton’s third law of motion by saying that ‘action equals reaction’.
9. Four balls are dropped at the same time from the top of a very tall tower. There is no wind blowing.
   Which ball hits the ground first?
10. A nitrogen molecule P travelling at a speed of 320 m s–1 in a vacuum collides with a stationary nitrogen molecule Q.

1. A charged particle is placed in a uniform field of force. The direction of the force on the particle is opposite to the direction of the field.
2. A disc of radius r is acted upon by two opposite forces, each of magnitude F. The forces form a couple, as shown.
3. A uniform square sign of weight 40 N is suspended vertically from its top edge by a horizontal hinge, as shown.
4. Each foot of an elephant has a circular cross-section with a circumference of 1.4 m. The elephant has a mass of 5400 kg.
5. A stone is falling vertically through the air at a constant (terminal) velocity.
6. An object of weight 12 N rests on a platform on top of a container with two pistons, as shown. The container contains a fixed mass of gas, and the pistons are free to move.
7. A constant force F, acting on a car of mass m, moves the car up a slope through a distance s at constant velocity v. The angle of the slope to the horizontal is .
8. What is the definition of power?
9. A steel bar of circular cross-section is under tension T, as shown
10. Two guitar strings are stretched by tensile forces.
11. Two lasers emit light in a vacuum. One laser emits red light and the other emits green light.
12. Two particles in a progressive wave are a distance 10 cm apart. The two graphs show the variation with time t of the displacement d of the two particles.
13. A sound wave is detected by a microphone that is connected to a cathode-ray oscilloscope (CRO).
14. A person stands at the side of a straight railway track. A train moves towards the person and emits sound from its whistle. The person hears a sound of frequency 1690 Hz as the train approaches him.
15. Which list shows electromagnetic waves in order of decreasing frequency?
16. A pipe of length L is open at one end and closed at the other end. A loudspeaker is at the open end and emits a sound wave into the pipe. Which list shows these four regions in order of increasing wavelength?
17. Which diagram best shows how water waves diffract when they pass through a gap in a barrier?
18. In a two-source interference experiment, light of a single frequency is incident on a double slit.
19. A parallel beam of light consists of light of wavelength 420 nm and light of wavelength 630 nm Which change would cause the distance between the bright lines on the screen to be reduced?
20. A positively charged particle P is in an electric field, as shown
21. The diagram shows two parallel metal plates P and Q, separated by a distance of 5.0 mm. There is a potential difference of 700V between the plates. Plate Q is earthed.
22. A wedge-shaped metal conductor of length L, varying width and uniform thickness is connected to a cell, as shown.
23. The power output of an electrical supply is 2.4 kW at a potential difference (p.d.) of 240V. The two wires between the supply and a kettle each have a resistance of 0.50, as shown.
24. The graph shows the variation with potential difference V of the current I in components X, Y and Z.
25. A wire of resistance 9.55 has a diameter of 0.280 mm.
26. A cell of constant electromotive force (e.m.f.) but with internal resistance is connected to a fixed resistor R using a potentiometer. A voltmeter measures the potential difference (p.d.) between the terminals of the cell.
27. A cell of electromotive force (e.m.f.) E and negligible internal resistance is connected to a circuit.
28. Two resistors are connected in series with a 6.0V power supply, as shown.
29. A nucleus of magnesium decays into a nucleus X by emitting a + particle. The decay is represented by the equation shown.
30. In – decay, a neutron inside a nucleus changes to a proton.

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Paper 2

Question 1

(a)

Difference between scalar quantity and vector quantity:

A scalar quantity has a magnitude only while a vector quantity has both a magnitude and a direction

(b)

2 forces of magnitude 6.0N and 8.0N act at point P. both forces act away from point P and angle between them is 40o. Fig shows 2 lines at angle of 40o to one another. On Fig, draw vector diagram to determine magnitude of resultant of 2 forces:

The diagram has a correct shape (parallelogram or triangle) with the arrows in the correct directions (parallel to the given ones)

(Note that the dotted lines do not represent the size of the 2 vectors mentioned – you need to choose the appropriate scale)

Resultant = 13.2 ± 0.2 N

Question 2

Question 3

Student has been asked to determine linear acceleration of toy car as it moves down a slope. He sets up apparatus as shown.

Time t to move from rest through a distance d found for different values of d. Graph of d (y-axis) plotted against t2 (x-axis) as shown.

(a)

Theory suggests that graph is a straight line through origin. Name feature on Fig that indicates presence of

(i)

Random error:

The scatter of points (about the line)

(ii)

Systematic error:

The intercept (on the t2 axis)

(b)

(i)

Gradient of line of graph in Fig:

Gradient = Δy / Δx = (100 – 0) / (10.0 – 0.6) = 10.6 (cms-2)

(ii)

Use answer to (i) to calculate acceleration of toy down slope:

s = ut + ½ at2

(½ a = gradient) So, acceleration = 2 x gradient

Acceleration = 0.212ms‑2

Question 4

Ball has mass m. it is dropped onto horizontal plate as shown. Just as the ball makes contact with plate, it has velocity v, momentum p and kinetic energy Ek.

(a)

(i)

Expression for momentum p in terms of m and v:

p = mv

(ii)

Show that kinetic energy given by Ek = p2 / 2m:

Ek = ½ mv2

Algebra leading to (e.g. p = mv and v = p/m)

Ek = p2/2m

(b)

Just before impact with plate, ball of mass 35g has speed 4.5ms-1. It bounces from plate so that its speed immediately after losing contact with plate is 3.5ms-1. Ball is on contact with plate for 0.14s.

For time that ball is in contact with plate,

(i)

Average force, in addition to weight of ball, that plate exerts on ball:

EITHER

Δp = 0.035(4.5 + 3.5) = 0.28Ns

Force = Δp / Δt (= 0.28 / 0.14) = 2.0N

OR

a = (4.5 – (-3.5)) / 0.14 = 57.1ms-2

F = ma (= 0.035 x 575.1) = 2.0N

(ii)

Loss in kinetic energy of ball:

Loss in kinetic energy = ½ (0.035) (4.52 – 3.52) = 0.14J

(c)

Explain whether linear momentum conserved during bounce:

The plate (and Earth) gain momentum which is equal and opposite to the change for the ball. So, momentum is conserved.

Question 5

2 forces, each of magnitude F, form a couple acting on the edge of disc of radius r, as shown.

(a)

Disc is made to complete n evolutions about axis through its centre, normal to plane of disc. Expression:

(i)

Distance moved by point on circumference of disc:

Distance = n(2πr) = 2πnr

(ii)

Work done by 1 of the 2 forces:

Work done = F x (2πnr)

(b)

Using answer to (a), show that work W done by couple producing torque T when it turns through n revolutions given by          W = 2πnT:

Total work done = 2 x F x 2πnr

But the Torque T = 2Fr

Hence, work done = 2πnT

(c)

Car engine produces torque of 470Nm at 2400 revolutions per minute. Output power of engine:

Power = Work done / time (= 470 x 2π x 2400 / 60) = 1.2x105W

Question 6

Question 7

Household electric lamp rated as 240V, 60W. Filament of lamp made from tungsten and is a wire of constant radius 6.0x10-6m. Resistivity of tungsten at normal operating temperature of lamp is 7.9x10-7Ωm.

(a)

For lamp at its normal operating temperature:

(i)

Current in lamp:

P = VI

So, current I = P / V = 60 / 240 = 0.25A

(ii)

Show that resistance of filament is 960Ω:

Resistance, R (= V/I) = 240 / 0.25 = 960Ω

(b)

Length of filament:

R = ρL / A       (wrong formula, 0/3)

960 = (7.9x10-7) L / (π{6.0x10-6}2)

Length of filament, L = 0.137m

(c)

Comment on answer to (b):

Example:

The filament must be coiled / it is long for a lamp

Question 8

Thermistor has resistance 3900Ω at 0oC and resistance 1250Ω at 30oC. Thermistor connected into circuit of Fig in order to monitor temperature changes. Battery of e.m.f. 1.50V has negligible internal resistance and voltmeter has infinite resistance.

(a)

Voltmeter is to read 1.00V at 0oC. Show that resistance of resistor R is 7800Ω:

V / E = R / Rtot                        or 0.5 = I x 3900

1/0/1.5 = R / (R+3900)            or 1.0 = 0.5R / 3900

R = 7800Ω                              or R = 7800Ω

(b)

Temperature of thermistor increased to 30oC. Reading on voltmeter:

EITHER

V = 1.5 x [7800 / (7800+1250)] = 1.29V

OR

I = 1.5 / (7800+1250)              (=1.66x10-4A)

V = IR (= (1.66x10-4)x7800) = 1.29

(c)

Voltmeter in Fig replaced with one having resistance of 7800Ω. Reading on this voltmeter for thermistor at temperature of 0oC:

Combined resistance of resistor R and voltmeter (= [1/7800 + 1/7800]-1) = 3900Ω

So, reading at 0oC (= [3900 / (3900+3900)]x1.5 ) = 0.75V