Momentum

WPH11Topic 1.33 questions

Momentum as $p = mv$ and the conservation of linear momentum in one dimension.

Specification points

Understand that momentum is defined as $p = mv$
Know the principle of conservation of linear momentum, understand how to relate this to Newton's laws of motion and understand how to apply this to problems in one dimension

Get a plain-language explanation, a worked example and the usual mistake.

Original practice questions written in the style of the exam.

Question 14 marks
A trolley of mass $0.80\,\text{kg}$ moving at $1.5\,\text{m s}^{-1}$ collides with a stationary trolley of mass $1.2\,\text{kg}$ . The trolleys stick together.

(a) Calculate the velocity of the trolleys immediately after the collision.

(b) Calculate the kinetic energy lost in the collision.
Mark scheme
- Momentum before $= 0.80 \times 1.5 = 1.2\,\text{kg m s}^{-1}$ (1)
- $v = 1.2/2.0 = 0.60\,\text{m s}^{-1}$ (1)
Question 23 marks
A tennis ball of mass $0.057\,\text{kg}$ hits a wall horizontally at $22\,\text{m s}^{-1}$ and rebounds along the same line at $18\,\text{m s}^{-1}$ . The ball is in contact with the wall for .

1.2/2.0=

0.60m s−1

KE before

= \tfrac{1}{2}(0.80)(1.5)^2 = 0.90\,\text{J}

and KE after

= \tfrac{1}{2}(2.0)(0.60)^2 = 0.36\,\text{J}

(1)

KE lost

= 0.54\,\text{J}

(1)

−1

0.015\,\text{s}

Calculate the average force exerted on the ball by the wall.

Mark scheme

Change in velocity $= 18 - (-22) = 40\,\text{m s}^{-1}$ (direction reverses) (1)
Change in momentum $= 0.057 \times 40 = 2.28\,\text{kg m s}^{-1}$ (1)
$F = \Delta p/\Delta t = 2.28/0.015 = 150\,\text{N}$ (152 N) (1)