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Date November 2020 Marks available 3 Reference code 20N.2.SL.TZ0.2
Level Standard level Paper Paper 2 Time zone 0 - no time zone
Command term Deduce Question number 2 Adapted from N/A

Question

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.

Draw and label the free-body diagram for the person.

 

[2]
a.

The person must not slide down the wall. Show that the minimum angular velocity ω of the cylinder for this situation is

ω=gμR

where μ is the coefficient of static friction between the person and the cylinder.

[2]
b.

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

[3]
c.

Markscheme

arrow downwards labelled weight/W/mg and arrow upwards labelled friction/F 

arrow horizontally to the left labelled «normal» reaction/N 


Ignore point of application of the forces but do not allow arrows that do not touch the object.

Do not allow horizontal force to be labelled ‘centripetal’ or R.

a.

See F=μN AND N=mRω2 

«substituting for N» μmω2R=mg 

b.

ALTERNATIVE 1

minimum required angular velocity «=9.810.40×3.5»=2.6«rads-1» 

actual angular velocity «=2π6028»=2.9«rads-1»

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

 

ALTERNATIVE 2

Minimum friction force =mg=«9.81m» 

Actual friction force «=μmRω2=0.40m×3.52π28602»=12.0m 

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

 

Allow 2.7 from g=10ms-2.

c.

Examiners report

[N/A]
a.
[N/A]
b.
[N/A]
c.

Syllabus sections

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