9702/May Jun/42/2010/Q10

(a) State the name of an electrical sensing device that will respond to changes in
(i) length,
(ii) pressure.

(b) A relay is sometimes used as the output of a sensing circuit.
The output of a particular sensing circuit is either + 2 V or – 2 V.
On Fig. 10.1, draw symbols for a relay and any other necessary component so that the
external circuit is switched on only when the output from the sensing circuit is + 2 V.

Solution:

(a)

(i) Strain gauge

(ii) Piezo-electric / quartz crystal / transducer

(b) For the circuit, a coil of relay is connected between the sensing circuit output and earth and the switch is across the terminals of the external circuit.

A diode is connected in series with the coil with a correct polarity for the diode (downwards). A second diode with correct polarity is connected (upwards and parallel to coil of relay).

{Note that the following explanations have been taken directly from the application booklet.

The diode D₁ conducts only when the output is positive with respect to earth and thus the relay coil is energized only when the output is positive. When the current in the relay coil is switched off, a back e.m.f. is generated in the coil that could damage the sensing circuit. A diode D₂ is connected across the coil to protect the sensing circuit from this back e.m.f.}

Reference: PYQ - May/June 2010 Paper 42 Q10

Reference links:

https://electronics.stackexchange.com/questions/100134/why-is-there-a-diode-connected-in-parallel-to-a-relay-coil
https://electronics.stackexchange.com/questions/56322/do-i-need-a-flyback-diode-with-an-automotive-relay/56323#56323

9702/Oct Nov/13/2017/Q10

Two railway trucks of masses m and 3m move towards each other in opposite directions with speeds 2v and v respectively. These trucks collide and stick together.

What is the speed of the trucks after the collision?

Solution:
Answer: A

In order to solve this question we need to use the principle of conservation of momentum which states:

The momentum in a closed system remains constant before and after a collision or explosion.

I.E.

momentum before=momentum after

And ingeneral momentum is calculated using: P=mv where P is the momentum, m is the mass of the object, and v is the velocity of the object.

Hence the total momentum before the collision is:

P1+P2
=(m x 2v) + (3m x (-v))

NOTE: notice the negative v on the second truck as it is moving in the opposite direction to the first truck
=-mv

After the collision the the trucks stick together so the total mass becomes 4m and the combined trucks move at an unknown speed of v_​after

We will solve the equation for conservation of momentum to determine v_after​:

mv=4mv_after

cancelling out the m's:

v=4v_after

and rearranging to make v_​after the subject of the equation:

v_after​=0.25v

Which is our final answer.

Reference: PYQ - Oct/Nov 2017 Paper 13 Q10