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 Forces: 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 B on A, we use the formula for impulse: $I = m(v_f - v_i)$

Where:

$m$ is the mass of A, which is 0.3 kg
$v_f$ is the final velocity of A after the collision, which is -2 m/s (the negative sign indicates the direction change)
$v_i$ is the initial velocity of A before the collision, which is 8 m/s.

Substituting the values into the impulse equation: $I = 0.3 imes (-2 - 8) = 0.3 imes (-10) = -3 ext{ Ns}$

Therefore, the magnitude of the impulse exerted by B on A is 3 Ns.

Step 2

b) the value of m

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Answer

Using the law of conservation of momentum, the momentum before the collision must equal the momentum after the collision.

Before the collision, the total momentum (P_initial) is:
$P_{initial} = m (-4) + 0.3 (8)$

After the collision, the total momentum (P_final) is:
$P_{final} = m (2) + 0.3 (-2)$

Setting the two equal gives us:
$m(-4) + 0.3(8) = m(2) + 0.3(-2)$

Simplifying this equation: $-4m + 2.4 = 2m - 0.6$

Combining like terms: $-4m - 2m = -0.6 - 2.4$
$-6m = -3$
$m = 0.5$

Thus, the value of m is 0.5 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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