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Question 18M.3.SL.TZ2.6a.ii

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Date May 2018 Marks available [Maximum mark: 3] Reference code 18M.3.SL.TZ2.6a.ii
Level SL Paper 3 Time zone TZ2
Command term Show that Question number a.ii Adapted from N/A
a.ii.
[Maximum mark: 3]
18M.3.SL.TZ2.6a.ii

A wheel of mass 0.25 kg consists of a cylinder mounted on a central shaft. The shaft has a radius of 1.2 cm and the cylinder has a radius of 4.0 cm. The shaft rests on two rails with the cylinder able to spin freely between the rails.

M18/4/PHYSI/SP3/ENG/TZ2/06

The stationary wheel is released from rest and rolls down a slope with the shaft rolling on the rails without slipping from point A to point B.

M18/4/PHYSI/SP3/ENG/TZ2/06.a

(a.ii)

In moving from point A to point B, the centre of mass of the wheel falls through a vertical distance of 0.36 m. Show that the translational speed of the wheel is about 1 m s–1 after its displacement.

[3]

Markscheme

ΔKE + Δrotational KE = ΔGPE

OR

1 2 mv2 + 1 2 I v 2 r 2 = mgh

 

1 2  × 0.250 × v2 +  1 2  × 1.3 × 10–4 ×  v 2 1.44 × 10 − 4 = 0.250 × 9.81 × 0.36

v = 1.2 «m s–1»

 

[3 marks]

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