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Two particles A and B, of mass 0.3 kg and m kg respectively, are moving in opposite directions along the same straight horizontal line so that the particles collide directly - Edexcel - A-Level Maths Mechanics - Question 2 - 2007 - Paper 1
Question 2
Two particles A and B, of mass 0.3 kg and m kg respectively, are moving in opposite directions along the same straight horizontal line so that the particles collide ... show full transcript
Worked Solution & Example Answer:Two particles A and B, of mass 0.3 kg and m kg respectively, are moving in opposite directions along the same straight horizontal line so that the particles collide directly - Edexcel - A-Level Maths Mechanics - Question 2 - 2007 - Paper 1
Step 1
a) the magnitude of the impulse exerted by B on A in the collision
Answer
The impulse (I) can be calculated using the change in momentum. For particle A:
Here:
- Mass of A, ( m_A = 0.3 \text{ kg} )
- Initial velocity of A, ( v_{A_{initial}} = 8 \text{ m s}^{-1} )
- Final velocity of A after collision, ( v_{A_{final}} = -2 \text{ m s}^{-1} ) (negative because direction is reversed)
Calculating the impulse:
Since we are interested in magnitude, the impulse exerted by B on A is 3 Ns.
Step 2
b) the value of m
Answer
Using the law of conservation of momentum before and after the collision:
Before collision:
- Momentum of A, ( p_A = m_A imes v_A = 0.3 imes 8 = 2.4 \text{ kg m s}^{-1} )
- Momentum of B, ( p_B = m imes v_B = m imes (-4) = -4m \text{ kg m s}^{-1} ) (negative since it's in the opposite direction)
Total momentum before collision:
After collision:
- Momentum of A, ( p_{A_{final}} = 0.3 imes (-2) = -0.6 \text{ kg m s}^{-1} )
- Momentum of B, ( p_{B_{final}} = m imes 2 = 2m \text{ kg m s}^{-1} )
Total momentum after collision:
Setting initial momentum equal to final momentum:
Rearranging gives:
Thus,