9702/Oct Nov/13/2013/Q22

A lift is supported by two steel cables each of length 20 m.

Each of the cables consists of 100 parallel steel wires, each wire of cross-sectional area 3.2×10^–6 m². The Young modulus of steel is 2.1×10¹¹Nm^–2.

Which distance does the lift move downward when a man of mass 70 kg steps into it?
A 0.010 mm

B 0.020 mm

C 0.10 mm

D 0.20 mm

Solution:

Answer: C

Hooke’s law: F = ke

The lift is supported by 2 steel cables, each of which consists of 100 parallel steel wires. So, there is a total of 200 parallel steel wires in parallel.

For parallel spring,
Effective spring constant, k_eff = k₁ + k₂ + k₃ + … 

First, we need to find the spring constant, k for 1 steel wire.

For 1 wire,
Young modulus, E = stress / strain = (F/A) / (e/L) = FL / Ae
Hooke’s law: F = ke
Young modulus, E = (ke)L / Ae = kL / A
Spring constant, k = EA / L = (2.1 × 10¹¹) (3.2 × 10^–6) / 20 = 33600 Nm^-1 

Effective spring constant, k_eff = 200k
Hooke’s law: F = k_eff e
Mass of person = 70kg. Weight = mg = 700N           (take g = 10 ms^-2)
Extension, e = F / k_eff = 700 / (200 × 33600) = 0.00010m = 0.10 mm

Reference: PYQ - Oct/Nov 2013 Paper 13 Q22

9702/Oct Nov/13/2017/Q22

The graph shows how the displacement of a particle in a wave varies with time.

Which statement is correct?
A The wave has a period of 2 s and could be either transverse or longitudinal.
B The wave has a period of 2 s and must be transverse.
C The wave has a period of 4 s and could be either transverse or longitudinal.
D The wave has a period of 4 s and must be transverse.

Solution:

Answer: C

The period of the wave is 4s, so option A and B are incorrect.

The wave could be either transverse or longitudinal because the graph is not represent the actual shape of the longitudinal wave. Because the graph is only represent the displacement of the wave during specific time.

Reference: PYQ - Oct/Nov 2017 Paper 13 Q22

9702/Oct Nov/12/2017/Q22

When sound travels through air, the air particles vibrate. A graph of displacement against time for
a single air particle is shown.

Which graph best shows how the kinetic energy of the air particle varies with time?

Solution:

Answer: D

Kinetic energy = ½ mv²

A graph of displacement against time for a single air particle is shown.  The gradient of the displacement-time graph gives the velocity of the air particle at that point in time. This is done by calculating the gradient of the tangent at that point.

The gradient (and hence, velocity) is found to be zero at the maximum displacement (the tangent is horizontal) and maximum when the displacement is zero (the tangent is steepest).

Thus, at time = 0, T and 2T the velocity is zero and hence kinetic energy is zero. [A and C incorrect]

But, between time = 0 and T or between time = T and 2T the displacement is zero (in case) twice. So, the velocity (and kinetic energy) reaches its maximum value 2 times in each of the 2 intervals.[B is incorrect]

Reference: PYQ - Oct/Nov 2017 Paper 12 Q22