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Two particles P and Q have masses 4m and m respectively - Edexcel - A-Level Maths: Mechanics - Question 1 - 2013 - Paper 1
Question 1
Two particles P and Q have masses 4m and m respectively. The particles are moving towards each other on a smooth horizontal plane and collide directly. The speeds of... show full transcript
Worked Solution & Example Answer:Two particles P and Q have masses 4m and m respectively - Edexcel - A-Level Maths: Mechanics - Question 1 - 2013 - Paper 1
Step 1
Find the speed and direction of motion of Q after the collision.
Answer
To find the speed and direction of Q after the collision, we apply the principle of conservation of momentum. The total momentum before the collision must equal the total momentum after the collision.
Before the collision:
- Momentum of P: (4m \cdot 2u = 8mu)
- Momentum of Q: (m \cdot 5u = 5mu)
- Total momentum before: (8mu + 5mu = 13mu)
After the collision, the momentum of P will be negative due to its reversal:
- Momentum of P: (4m \cdot -\frac{1}{2}u = -2mu)
- Let the velocity of Q after the collision be (v); then the momentum of Q will be (m \cdot v) .
- Total momentum after: (-2mu + mv)
Setting total momentum before equal to total momentum after: [ 13mu = -2mu + mv ] [ 15mu = mv ] [ v = 15u ] Thus, Q moves at (15u) in the same direction as it was moving before the collision.
Step 2
Find the magnitude of the impulse exerted on P by Q in the collision.
Answer
The impulse exerted on P by Q is defined by the change in momentum of P. We can express impulse (I) mathematically as:
[ I = \Delta p_P = p_{P_{after}} - p_{P_{before}} ]
Calculating the momentum before the collision for P: [ p_{P_{before}} = 4m \cdot 2u = 8mu ]
After the collision: [ p_{P_{after}} = 4m \cdot (-\frac{1}{2}u) = -2mu ]
Thus, [ I = -2mu - 8mu = -10mu ] Taking the magnitude: [ |I| = 10mu ] Therefore, the magnitude of the impulse exerted on P by Q in the collision is (10mu).