• Physics 9702 Doubts | Help Page 187

Question 912: [Oscillations > Simple harmonic motion]

A student sets out to investigate the oscillation of a mass suspended from the free end of a spring, as illustrated in Fig.1.

The mass is pulled downwards and then released. The variation with time t of the displacement y of the mass is shown in Fig.2.

(a) Use information from Fig.2

(i) to explain why the graph suggests that the oscillations are undamped,

(ii) to calculate angular frequency of the oscillations,

(iii) to determine maximum speed of the oscillating mass.

(b)

(i) Determine resonant frequency f₀ of the mass-spring system.

(ii) The student finds that if short impulsive forces of frequency ½ f₀ are impressed on the mass-spring system, a large amplitude of oscillation is obtained. Explain this observation.

Reference: Past Exam Paper – November 2002 Paper 4 Q3

Solution 912:

(a)

(i) It has a constant amplitude.

(ii)

Period T = 0.75s

Angular frequency ω = 2π / T = 8.4 rad s^–1

(iii)

EITHER use of gradient         OR v = ωy₀

{y₀ is the amplitude}

Maximum speed v = {8.4 × 0.02 =} 0.168 m s^–1

(b)

(i) Resonant frequency f₀ {= 1/T = 1/0.75} = 1.3Hz

(ii) At ½ f₀, a ‘pulse’ is provided to the mass on alternate/some oscillations. So, the ‘pulses’ build up the amplitude.

Question 913: [Current of Electricity]

(a) Distinguish between potential difference (p.d.) and electromotive force (e.m.f.) in terms of energy transformations.

(b) Two cells A and B are connected in series with a resistor R of resistance 5.5 Ω, as shown in Fig.1.

Cell A has e.m.f. 4.4 V and internal resistance 2.3 Ω. Cell B has e.m.f. 2.1 V and internal resistance 1.8 Ω.

(i) State Kirchhoff’s second law.

(ii) Calculate current in the circuit.

(iii) On Fig.1, draw an arrow to show the direction of the current in the circuit. Label this arrow I.

(iv) Calculate

1. p.d. across resistor R,

2. terminal p.d. across cell A,

3. terminal p.d. across cell B.

Reference: Past Exam Paper – November 2011 Paper 23 Q4

Solution 913:

(a)

Potential difference (p.d.) is the energy transformed from electrical to other forms, per unit charge.

Electromotive force (e.m.f.) is the energy transformed from other forms to electrical per unit charge.

(b)

(i) Kirchhoff’s second law states that the sum of e.m.f.s (in a closed circuit) is equal to the sum of potential differences.

(ii)

4.4 – 2.1 = I × (1.8 + 5.5 + 2.3)

Current I = 0.24 A

(iii) The arrow (labelled) I should be shown anticlockwise.

(iv)

1. V = I × R = 0.24 × 5.5 = 1.3(2) V

2. V_A = 4.4 – (I × 2.3) = 3.8(5) V

{Voltage loss in cell A = I × 2.3}

3.

EITHER V_B = 2.1 + (I × 1.8)                         OR V_B = 3.8 – 1.3

{Here, we need to add (I × 1.8) to the e.m.f. of cell B because the current is flowing towards the positive terminal of cell B.}

V_B = 2.5(3) V

Question 914: [Dynamics > Moments]

Which pair of forces acts as a couple on the circular object?

Reference: Past Exam Paper – November 2008 Paper 1 Q14

Solution 914:

Answer: A.

A couple consists of 2 forces, equal in magnitude. But acting in opposite directions, so that they produce a resultant turning effect. Thus, these 2 forces produces a resultant moment, while the resultant force is zero.

Choice B: both forces are in the same direction + their magnitudes are not equal

Choice C: different magnitudes

Choice D: directions are not opposite to each other

Question 915: [Kinetic theory of Gases]

(a)

(i) State the basic assumption of the kinetic theory of gases that leads to the conclusion that potential energy between the atoms of an ideal gas is zero.

(ii) State what is meant by the internal energy of a substance.

(iii) Explain why an increase in internal energy of an ideal gas is directly related to a rise in temperature of the gas.

(b) A fixed mass of an ideal gas undergoes a cycle PQRP of changes as shown in Fig.1.

(i) State the change in internal energy of the gas during one complete cycle PQRP.

(ii) Calculate work done on the gas during the change from P to Q.

(iii) Some energy changes during the cycle PQRP are shown in Fig.2.

Complete Fig.2 to show all of the energy changes.

Reference: Past Exam Paper – November 2010 Paper 41 & 42 Q2

Solution 915:

A fixed mass of an ideal gas undergoes a cycle PQRP of changes as shown in Fig. 2.1.