Particle P has mass 3 kg and particle Q has mass 2 kg. The particles are moving in opposite directions on a smooth horizontal plane when they collide directly. Immediately before the collision, P has speed 3 m s⁻¹ and Q has speed 2 m s⁻¹. Immediately after the collision, both particles move in the same direction and the difference in their speeds is 1 m s⁻¹. (a) Find the speed of each particle after the collision. (b) Find the magnitude of the impulse exerted on P by Q.

A-Level Edexcel Maths Mechanics Newtons Second Law: Particle P has mass 3 kg and par

Particle P has mass 3 kg and particle Q has mass 2 kg - Edexcel - A-Level Maths Mechanics - Question 2 - 2011 - Paper 1

Question 2

Particle P has mass 3 kg and particle Q has mass 2 kg. The particles are moving in opposite directions on a smooth horizontal plane when they collide directly. Immed... show full transcript

Worked Solution & Example Answer:Particle P has mass 3 kg and particle Q has mass 2 kg - Edexcel - A-Level Maths Mechanics - Question 2 - 2011 - Paper 1

Step 1

Find the speed of each particle after the collision.

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Answer

Let the speed of particle P after the collision be denoted as $v$ (m/s). Then the speed of particle Q after the collision is $v - 1$ (m/s) since the difference in their speeds is 1 m/s.

Using the principle of conservation of linear momentum:

$3 \cdot 3 + 2 \cdot (-2) = 3v + 2(v - 1)$

This gives: $9 - 4 = 3v + 2v - 2$
$5 = 5v - 2$
$5 + 2 = 5v$
$7 = 5v$
$v = 1.4\, \text{m/s}$

Thus, particle P has speed $1.4\, \text{m/s}$ after the collision and particle Q has speed $0.4\, \text{m/s}$ after the collision.

Step 2

Find the magnitude of the impulse exerted on P by Q.

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Answer

Impulse is given by the change in momentum, which can be expressed as:

$J = m(v_f - v_i)$

Where:

$m$ is the mass of the particle (here, particle P has mass 3 kg).
$v_f$ is the final velocity of particle P ( $1.4\, \text{m/s}$ ).
$v_i$ is the initial velocity of particle P ( $3\, \text{m/s}$ ).

Therefore, the impulse exerted on particle P by particle Q is:

$J = 3(1.4 - 3) = 3 \cdot (-1.6) = -4.8\, \text{Ns}$

The magnitude is: $|J| = 4.8\, \text{Ns}$

Particle P has mass 3 kg and particle Q has mass 2 kg - Edexcel - A-Level Maths Mechanics - Question 2 - 2011 - Paper 1

Worked Solution & Example Answer:Particle P has mass 3 kg and particle Q has mass 2 kg - Edexcel - A-Level Maths Mechanics - Question 2 - 2011 - Paper 1

Find the speed of each particle after the collision.

Find the magnitude of the impulse exerted on P by Q.

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