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. Immediately before the collision, the speeds of A and B are 8 m s⁻¹ and 4 m s⁻¹ respectively. In the collision the direction of motion of each particle is reversed and, immediately after the collision, the speed of each particle is 2 m s⁻¹. Find (a) the magnitude of the impulse exerted by B on A in the collision, (b) the value of m.

A-Level Edexcel Maths Mechanics Newtons Second Law: Two particles A and B, of mass 0

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

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Answer

To find the impulse exerted by particle B on A, we use the impulse-momentum theorem, which states that the impulse is equal to the change in momentum:

$I = ext{Change in momentum} = m(v_f - v_i)$

For particle A:

Mass (m_A) = 0.3 kg
Initial speed of A (v_{iA}) = 8 m s⁻¹ (towards the left)
Final speed of A (v_{fA}) = -2 m s⁻¹ (towards the right, thus negative)

Change in momentum of A: $ext{Change in momentum of A} = 0.3(-2 - 8) = 0.3(-10) = -3 ext{ Ns}$

Thus, the magnitude of the impulse exerted by B on A is:

$|I| = 3 ext{ Ns}$

Step 2

(b) the value of m

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Answer

To find the mass m of particle B, we can use the principle of conservation of momentum before and after the collision:

$ext{Initial momentum} = ext{Final momentum}$

Initial momentum:

Momentum of A = 0.3 kg × 8 m s⁻¹ = 2.4 kg m s⁻¹ (to the left)
Momentum of B = m × (-4) m s⁻¹ = -4m kg m s⁻¹ (to the right)

Total initial momentum: $P_{initial} = 2.4 - 4m$

Final momentum:

Final momentum of A = 0.3 kg × (-2) m s⁻¹ = -0.6 kg m s⁻¹
Final momentum of B = m × 2 m s⁻¹ = 2m kg m s⁻¹

Total final momentum: $P_{final} = -0.6 + 2m$

Setting initial momentum equal to final momentum: $2.4 - 4m = -0.6 + 2m$

Solving for m: $2.4 + 0.6 = 4m + 2m$ $3 = 6m$ $m = 0.5 ext{ kg}$

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

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

(a) the magnitude of the impulse exerted by B on A in the collision

(b) the value of m

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