Two particles A and B have masses 4 kg and m kg respectively. They are moving towards each other in opposite directions on a smooth horizontal table when they collide directly. Immediately before the collision, the speed of A is 5 m s⁻¹ and the speed of B is 3 m s⁻¹. Immediately after the collision, the direction of motion of A is unchanged and the speed of A is 1 m s⁻¹. (a) Find the magnitude of the impulse exerted on A in the collision. (b) Find the value of m.

A-Level Edexcel Maths Mechanics Newtons Second Law: Two particles A and B have masse

Two particles A and B have masses 4 kg and m kg respectively - Edexcel - A-Level Maths Mechanics - Question 1 - 2008 - Paper 1

Question 1

Two particles A and B have masses 4 kg and m kg respectively. They are moving towards each other in opposite directions on a smooth horizontal table when they collid... show full transcript

Worked Solution & Example Answer:Two particles A and B have masses 4 kg and m kg respectively - Edexcel - A-Level Maths Mechanics - Question 1 - 2008 - Paper 1

Step 1

(a) Find the magnitude of the impulse exerted on A in the collision.

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Answer

The impulse exerted on an object can be calculated using the formula:

$I = m(v_f - v_i)$

Where:

$I$ is the impulse,
$m$ is the mass,
$v_i$ is the initial velocity,
$v_f$ is the final velocity.

For particle A:

Mass $m_A = 4 ext{ kg}$ ,
Initial velocity $v_i = 5 ext{ m s}^{-1}$ (towards the right),
Final velocity $v_f = 1 ext{ m s}^{-1}$ (still towards the right).

Substituting the values into the impulse formula:

$I = 4(1 - 5) = 4(-4) = -16 ext{ Ns}$

The magnitude of the impulse is therefore:

$|I| = 16 ext{ Ns}$

Step 2

(b) Find the value of m.

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Answer

To find the value of m (the mass of particle B), we can apply the principle of conservation of momentum, which states:

$ext{Total momentum before collision} = ext{Total momentum after collision}$

Calculating the momentum before the collision:

Momentum of A before = $m_A imes v_A = 4 imes 5 = 20 ext{ kg m s}^{-1}$ (rightwards)
Momentum of B before = $m_B imes v_B = m imes (-3)$ (leftwards)

Thus, total momentum before collision is:

$P_{initial} = 20 - 3m$

Calculating momentum after the collision:

Momentum of A after = $4 imes 1 = 4 ext{ kg m s}^{-1}$ (rightwards)
Momentum of B after = $m imes 2$ (rightwards)

Thus, total momentum after collision is:

$P_{final} = 4 + 2m$

Equating initial and final momentum:

$20 - 3m = 4 + 2m$

Rearranging gives:

$20 - 4 = 2m + 3m$ $16 = 5m$

Solving for m: $m = rac{16}{5} = 3.2 ext{ kg}$

Two particles A and B have masses 4 kg and m kg respectively - Edexcel - A-Level Maths Mechanics - Question 1 - 2008 - Paper 1

Worked Solution & Example Answer:Two particles A and B have masses 4 kg and m kg respectively - Edexcel - A-Level Maths Mechanics - Question 1 - 2008 - Paper 1

(a) Find the magnitude of the impulse exerted on A in the collision.

(b) Find the value of m.

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