Further Mathematics · OCR H245 · Option M · Topic 6.03

Impulse and momentum

Linear momentum, impulse, restitution.

  • 3 sub-topics
  • 2 in Year 12, 1 in Year 13
  • 93 practice questions
  • 3 animated lessons
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What the specification says

Every sub-topic OCR can examine in this topic, with its reference number from the official specification. The Y12 and Y13 tags show when each sub-topic is usually taught.

  1. 6.03a-dLinear momentumY12
  2. 6.03e-hImpulseY13
  3. 6.03i-lRestitutionY12

Try 3 questions

Easy, medium and hard questions from this topic, each with a worked solutions and the mark for every step. All 93 questions in this topic, free, no account needed.

Momentum and impulse

Easy

Impulse · Year 12 · 1 mark

  1. A ball of mass 0.5 kg hits a wall at 10 m s⁻¹ and rebounds along the same line at 4 m s⁻¹. What is the magnitude of the impulse on the ball?
    (1)

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  1. The velocity changes direction, so the change in momentum is m(u+v)m(u + v).BB: 7.00 N s7.00\ \mathrm{N\,s}

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Momentum and impulse

Medium

Momentum and impulse · Year 12 · 6 marks

A ball of mass 0.2 kg moves horizontally with speed 10 m s⁻¹ towards a vertical wall. It hits the wall directly and rebounds with speed 4 m s⁻¹.
  1. (a)
    Find the magnitude of the impulse exerted on the ball by the wall.
    (3)
  2. (b)
    The ball is in contact with the wall for 0.02 s. Find the average force exerted by the wall.
    (1)
  3. (c)
    Find the kinetic energy lost in the impact.
    (2)
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Part (a)3 marks

  1. Take the rebound direction as positive: the velocity changes sign.I=m(v−u)=0.2(4−(−10))I = m(v - u) = 0.2(4 - (-10))
  2. =2.8 N s= 2.8\text{ N s}

Part (b)1 mark

  1. Impulse = force × time.2.80.02=140 N\frac{2.8}{0.02} = 140\text{ N}

Part (c)2 marks

  1. 12(0.2)(102−42)\tfrac{1}{2}(0.2)(10^2 - 4^2)
  2. =8.4 J= 8.4\text{ J}

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Elastic collisions in one dimension

Hard

Successive direct impacts · Year 12 · 7 marks

A sphere AA of mass 2m2m moves with speed 6 m s⁻¹ on a smooth horizontal floor and collides directly with a sphere BB of mass 6m6m, which is at rest. The coefficient of restitution between AA and BB is 23\frac{2}{3}. BB then hits a vertical wall at right angles; the coefficient of restitution between BB and the wall is 34\frac{3}{4}.
  1. (a)
    Find the speeds of AA and BB after their collision.
    (4)
  2. (b)
    Find the speed of BB after it rebounds from the wall.
    (1)
  3. (c)
    Determine whether there is a second collision between AA and BB.
    (2)
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Part (a)4 marks

  1. Momentum (the mass m cancels).6⋅2=2vA+6vB6 \cdot 2 = 2v_A + 6v_B
  2. Restitution.vB−vA=4v_B - v_A = 4
  3. vAv_A=−32, vB{}= - \frac{3}{2}, \ v_B=52{}= \frac{5}{2}

Part (b)1 mark

  1. 34×52\frac{3}{4} \times \frac{5}{2}=158{}= \frac{15}{8}

Part (c)2 marks

  1. Compare the velocities after B's rebound.A moves away from the wall at 32, B moves back at 158\text{A moves away from the wall at } \frac{3}{2}, \ \text{B moves back at } \frac{15}{8}
  2. BB is faster than AA, so it catches AA: a second collision.

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