• Physics 9702 Doubts | Help Page 188

Question 916: [Oscillations > Simple harmonic motion]

A vertical spring supports a mass, as shown in Fig.1.

 

The mass is displaced vertically then released. The variation with time t of the displacement y from its mean position is shown in Fig.2.

A student claims that the motion of the mass may be represented by the equation

y = y₀ sinωt.

(a) Give two reasons why the use of this equation is inappropriate.

                               

(b) Determine angular frequency ω of the oscillations.

(c) The mass is a lump of plasticine. The plasticine is now flattened so that its surface area is increased. The mass of the lump remains constant and the large surface area is horizontal.

The plasticine is displaced downwards by 1.5 cm and then released.

On Fig.2, sketch a graph to show the subsequent oscillations of the plasticine.

Reference: Past Exam Paper – June 2004 Paper 4 Q4

Solution 916:

(a)

Example:

The amplitude is not constant OR the wave is damped

It should be (-)cos, (not sin)

                               

(b)

Period T = 0.60 s

Angular frequency, ω = 2π / T = 10.5 rad s^–1 (allow 10.4 → 10.6)

(c)

The sketch should have:

same period

displacement always less

amplitude reducing appropriately

Question 917: [Matter > Deformation of Solids]

A spring of unextended length 0.50 m is stretched by a force of 2.0 N to a new length of 0.90 m.

Variation of its length with tension is as shown.

How much strain energy is stored in the spring?

A 0.40 J                       B 0.80 J                       C 0.90 J                       D 1.8 J

Reference: Past Exam Paper – June 2007 Paper 1 Q19

Solution 917:

Go to
A spring of unextended length 0.50 m is stretched by a force of 2.0 N to a new length of 0.90 m.

Question 918: [Kinematics > Terminal velocity]

Which displacement-time graph best represents the motion of a falling sphere, the initial acceleration of which eventually reduces until it begins to travel at constant terminal velocity?

Reference: Past Exam Paper – June 2009 Paper 1 Q5

Solution 918:

Answer: D.

The gradient of a displacement-time graph gives the velocity of the falling sphere.

For a constant terminal velocity, the gradient of the graph should become constant at the later stage. For the gradient to be constant, the graph should be a straight line in that region. Thus, the final section of the graph should be a straight line. [A and B are incorrect]

Terminal velocity is the maximum velocity reached by the falling sphere. It cannot be zero. A horizontal straight line indicates that the gradient is zero. [C is incorrect]

Question 919: [Alternating Current + Electromagnetism]

(a) The mean value of an alternating current is zero.

Explain

(i) why an alternating current gives rise to a heating effect in a resistor,

(ii) by reference to heating effect, what is meant by root-mean-square (r.m.s.) value of an alternating current.

(b) A simple iron-cored transformer is illustrated in Fig.1.

(i) State Faraday’s law of electromagnetic induction.

(ii) Use Faraday’s law to explain why the current in the primary coil is not in phase with the e.m.f. induced in the secondary coil.

Reference: Past Exam Paper – November 2014 Paper 41 & 42 Q7

Solution 919:

(a)

(i)

{Power loss in a resistor = I²R.}

EITHER The heating effect in a resistor ∝ (current)². But the square of value of an alternating current is always positive. So there is a heating effect.

OR The current moves in opposite directions in the resistor during half-cycles. The heating effect is independent of direction.

(ii) It is that value of the direct current, producing the same heating effect (as the alternating current) in a resistor.

(b)

(i) Faraday’s law of electromagnetic induction states that the induced e.m.f. is proportional to the rate of change of (magnetic) flux (linkage).

(ii) The flux in the core is in phase with the current in the primary coil. There is an (induced) e.m.f. in the secondary coil because the coil cuts the flux. The flux and the rate of change of flux are not in phase.