DP Physics (last assessment 2024)

Question 20N.2.SL.TZ0.c

Date	November 2020	Marks available	[Maximum mark: 3]	Reference code	20N.2.SL.TZ0.c
Level	SL	Paper	2	Time zone	TZ0
Command term	Deduce	Question number	c	Adapted from	N/A

[Maximum mark: 3]

20N.2.SL.TZ0.c

The Rotor is an amusement park ride that can be modelled as a vertical cylinder of inner radius $R$ rotating about its axis. When the cylinder rotates sufficiently fast, the floor drops out and the passengers stay motionless against the inner surface of the cylinder. The diagram shows a person taking the Rotor ride. The floor of the Rotor has been lowered away from the person.

The coefficient of static friction between the person and the cylinder is $0.40$ . The radius of the cylinder is $3.5 m$ . The cylinder makes $28$ revolutions per minute. Deduce whether the person will slide down the inner surface of the cylinder.

[3]

Markscheme

ALTERNATIVE 1

minimum required angular velocity $« = \sqrt{\frac{9.81}{0.40 \times 3.5}} » = 2.6 « rad s^{- 1} »$ ✓

actual angular velocity $« = \frac{2 π}{(\frac{60}{28})} » = 2.9 « rad s^{- 1} »$ ✓

actual angular velocity is greater than the minimum, so the person does not slide ✓

ALTERNATIVE 2

Minimum friction force $= m g = « 9.81 m »$ ✓

Actual friction force $« = μ m R ω^{2} = 0.40 m \times 3.5 {(2 π \frac{28}{60})}^{2} » = 12.0 m$ ✓

Actual friction force is greater than the minimum frictional force so the person does not slide ✓

Allow $2.7$ from $g = 10 m s^{- 2}$ .

Syllabus sections

Core

Core » Topic 6: Circular motion and gravitation » 6.1 – Circular motion

Core » Topic 2: Mechanics » 2.2 – Forces

Core » Topic 2: Mechanics

Core » Topic 6: Circular motion and gravitation

Question 20N.2.SL.TZ0.c

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