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Two particles P and Q have mass 0.4 kg and 0.6 kg respectively - Edexcel - A-Level Maths Mechanics - Question 1 - 2008 - Paper 1
Question 1
Two particles P and Q have mass 0.4 kg and 0.6 kg respectively. The particles are initially at rest on a smooth horizontal table. Particle P is given an impulse of m... show full transcript
Worked Solution & Example Answer:Two particles P and Q have mass 0.4 kg and 0.6 kg respectively - Edexcel - A-Level Maths Mechanics - Question 1 - 2008 - Paper 1
Step 1
Find the speed of P immediately before it collides with Q.
Answer
To find the speed of particle P before it collides with Q, we use the impulse-momentum theorem, which states that impulse equals the change in momentum.
Given that the impulse I is 3 N·s and the mass of particle P (m) is 0.4 kg, we can express this as:
Thus:
Now, solve for v:
Therefore, the speed of P immediately before it collides with Q is 7.5 m/s.
Step 2
Show that immediately after the collision P is at rest.
Answer
To analyze the collision, we apply the principle of conservation of momentum.
Let v be the speed of P immediately after the collision. The momentum before the collision is equal to the momentum after the collision:
Before collision:
- Momentum of P: (0.4 \times 7.5)
- Momentum of Q: 0 (initially at rest)
Total momentum before = 0.4 \times 7.5 + 0 = 3.0 , \text{kg·m/s}
After collision:
- Momentum of P: 0.4v
- Momentum of Q: 0.6 \times 5
Total momentum after = (0.4v + 0.6 \times 5)
Setting these equal gives us:
Rearranging this gives:
Thus:
This shows that immediately after the collision, particle P is at rest.