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Question 18M.2.HL.TZ2.1a.iii

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Date May 2018 Marks available [Maximum mark: 3] Reference code 18M.2.HL.TZ2.1a.iii
Level HL Paper 2 Time zone TZ2
Command term Show that Question number a.iii Adapted from N/A
a.iii.
[Maximum mark: 3]
18M.2.HL.TZ2.1a.iii

A small ball of mass m is moving in a horizontal circle on the inside surface of a frictionless hemispherical bowl.

M18/4/PHYSI/SP2/ENG/TZ2/01.a

The normal reaction force N makes an angle θ to the horizontal.

(a.iii)

Show that the magnitude of the net force F on the ball is given by the following equation.

                                          F = m g tan ⁡ θ

[3]

Markscheme

ALTERNATIVE 1

F = N cos θ

mg = N sin θ

dividing/substituting to get result

 

ALTERNATIVE 2

right angle triangle drawn with F, N and W/mg labelled

angle correctly labelled and arrows on forces in correct directions

correct use of trigonometry leading to the required relationship

 

M18/4/PHYSI/SP2/ENG/TZ2/01.a.ii

tan θ =  O A = m g F

[3 marks]

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