Two particles B and C have mass m kg and 3 kg respectively. They are moving towards each other in opposite directions on a smooth horizontal table. The two particles collide directly. Immediately before the collision, the speed of B is 4 m s⁻¹ and the speed of C is 2 m s⁻¹. In the collision the direction of motion of C is reversed and the direction of motion of B is unchanged. Immediately after the collision, the speed of B is 1 m s⁻¹ and the speed of C is 3 m s⁻¹. Find (a) the value of m, (b) the magnitude of the impulse received by C.

A-Level Edexcel Maths Mechanics Quantities, Units & Modelling: Two particles B and C have mass

Two particles B and C have mass m kg and 3 kg respectively - Edexcel - A-Level Maths Mechanics - Question 1 - 2011 - Paper 1

Question 1

Two particles B and C have mass m kg and 3 kg respectively. They are moving towards each other in opposite directions on a smooth horizontal table. The two particles... show full transcript

Worked Solution & Example Answer:Two particles B and C have mass m kg and 3 kg respectively - Edexcel - A-Level Maths Mechanics - Question 1 - 2011 - Paper 1

Step 1

(a) the value of m

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Answer

To find the value of m, we should apply the principle of conservation of momentum.

Step 1: Set up the equation

Before the collision, the momentum of B is given by:

$p_B = m_B v_B = m imes 4$

And the momentum of C is:

$p_C = m_C v_C = 3 imes (-2)$

(Here, C's velocity is negative because it is moving in the opposite direction.)

Step 2: Total momentum before collision

Setting the total momentum before collision equal to that after the collision:

total momentum before = total momentum after

$4m - 6 = m + 9$

Step 3: Solve for m

Rearranging the equation gives:

$4m - m = 9 + 6$

$3m = 15$

$m = 5$

Step 2

(b) the magnitude of the impulse received by C

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Answer

To find the impulse received by C, we need to calculate the change in momentum of C.

Step 1: Initial and final momentum of C

The initial momentum of C before the collision is:

$p_{C_{initial}} = m_C v_C = 3 imes (-2) = -6$

The final momentum of C after the collision is:

$p_{C_{final}} = m_C v_{C_{final}} = 3 imes 3 = 9$

Step 2: Calculate impulse

The impulse is given by the change in momentum:

$ext{Impulse} = p_{C_{final}} - p_{C_{initial}} = 9 - (-6) = 15$

Thus, the magnitude of the impulse received by C is 15.