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 Forces: 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

Find the magnitude of the impulse exerted on A in the collision.

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Answer

To find the impulse exerted on A, we can use the formula for impulse:

$I = m(v_f - v_i)$

where:

$I$ is the impulse,
$m$ is the mass of particle A (4 kg),
$v_f$ is the final velocity of A (1 m s⁻¹),
$v_i$ is the initial velocity of A (5 m s⁻¹).

Substituting the values into the formula:

$I = 4(1 - 5)$ $I = 4(-4)$ $I = -16 \, \text{Ns}$

The magnitude of the impulse is therefore $16 \, \text{Ns}$ .

Step 2

Find the value of m.

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Answer

Using the principle of conservation of momentum (CLM), we can express the momenta before and after the collision:

Before collision:

Momentum of A = $4 \times 5 = 20 \, \text{kg m s}^{-1}$ (to the right)
Momentum of B = $m \times (-3)$ (to the left)

After collision:

Momentum of A = $4 \times 1 = 4 \, \text{kg m s}^{-1}$ (to the right)
Momentum of B = $m \times 2$ (to the right)

Setting up the equation using conservation of momentum:

$20 - 3m = 4 + 2m$

Rearranging gives:

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

Solving for $m$ :

$m = \frac{16}{5} = 3.2 \, \text{kg}$

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

Find the magnitude of the impulse exerted on A in the collision.

Find the value of m.

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