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Date	November 2019	Marks available	2	Reference code	19N.2.SL.TZ0.1
Level	Standard level	Paper	Paper 2	Time zone	0 - no time zone
Command term	Calculate	Question number	1	Adapted from	N/A

Question

The graph shows the variation with time t of the horizontal force F exerted on a tennis ball by a racket.

The tennis ball was stationary at the instant when it was hit. The mass of the tennis ball is 5.8 × 10^–2 kg. The area under the curve is 0.84 N s.

Calculate the speed of the ball as it leaves the racket.

[2]

Show that the average force exerted on the ball by the racket is about 50 N.

[2]

Determine, with reference to the work done by the average force, the horizontal distance travelled by the ball while it was in contact with the racket.

[3]

Draw a graph to show the variation with t of the horizontal speed v of the ball while it was in contact with the racket. Numbers are not required on the axes.

[2]

Markscheme

links 0.84 to Δp ✔

$v =$ « $\frac{0.84}{5.8 \times 10^{- 2}} =$ » 14.5 «m s^–1»✔

NOTE: Award [2] for bald correct answer

use of Δt = «(28 – 12) × 10^–3=» 16 × 10^–3 «s» ✔

$\bar{F}$ =« $\frac{∆ p}{∆ t} =$ » $\frac{0.84}{16 \times 10^{- 3}}$ OR 53 «N» ✔

NOTE: Accept a time interval from 14 to 16 ms
Allow ECF from incorrect time interval

E_k= $\frac{1}{2}$ × 5.8 × 10^–2× 14.5²✔

E_k = W ✔

s = « $\frac{W}{F} = \frac{\frac{1}{2} \times 5.8 \times 10^{- 2} \times 14 . 5^{2}}{53} =$ » 0.12 « m » ✔

Allow ECF from (a) and (b)

Allow ECF from MP1

Award [2] max for a calculation without reference to work done, eg: average velocity × time

graph must show increasing speed from an initial of zero all the time ✔
overall correct curvature ✔

Examiners report

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Syllabus sections

Core » Topic 2: Mechanics » 2.4 – Momentum and impulse

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