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A particle P of mass 0.3 kg is moving with speed u m s⁻¹ in a straight line on a smooth horizontal table - Edexcel - A-Level Maths Mechanics - Question 4 - 2007 - Paper 1

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A particle P of mass 0.3 kg is moving with speed u m s⁻¹ in a straight line on a smooth horizontal table. The particle P collides directly with a particle Q of mass ... show full transcript

Worked Solution & Example Answer:A particle P of mass 0.3 kg is moving with speed u m s⁻¹ in a straight line on a smooth horizontal table - Edexcel - A-Level Maths Mechanics - Question 4 - 2007 - Paper 1

Step 1

Find the value of u

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Answer

To solve for the initial speed uu, we use the principle of conservation of linear momentum:

0.3u+0.6(0)=0.3(−2)+0.6(5)0.3u + 0.6(0) = 0.3(-2) + 0.6(5)

Substituting the masses gives:

0.3u = 2.4 \\ \therefore u = \frac{2.4}{0.3} = 8 \, \text{m s}^{-1}.$$

Step 2

Find the magnitude of the impulse exerted by P on Q

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Answer

The impulse II exerted by P on Q can be calculated using the change in momentum of Q:

I=Δp=m(vf−vi)=0.6(5−0)=3 Ns.I = \Delta p = m(v_f - v_i) = 0.6(5 - 0) = 3 \, \text{Ns}.

Step 3

Find the value of R

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Answer

We can use the equation of motion to find the force applied to Q.

From the equation: v=u+atv = u + at where v=0v = 0, u=5u = 5, and t=1.5t = 1.5,

we find acceleration aa:

\Rightarrow a = \frac{-5}{1.5} = -\frac{10}{3} \, \text{m s}^{-2}.$$ Using Newton's second law, $F = ma$: $$R = 0.6 \times (-\frac{10}{3}) = -2 \. \text{N}.$$ Thus, the magnitude of $R$ is $R = 2 \, ext{N}.$

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