Question

Ali is whirling a 2kg bunch of bananas on a smooth floor in a circular path having a radius of 0.50m. What force must he apply to keep the motion constant so that the bananas complete one revolution every 4 seconds?

A coin is on a turntable that rotates pi rad/s. The coefficient of static friction between the coin and the turntable is 0.25.
a. Calculation the maximum distance of the coin from the center of the turntable for it to move in a circle.
b. If the coin is placed at a distance of 4.7cm from the center of the turntable, what is the maximum speed of rotation of the turntable for the coin to move relative to the turntable without slipping?

Answer 1

1)Given mass,m=2 kg

radius, R =0.5m

Time Period =4 sec

Find Force

The Force that is applied here is centripetal Force F= mv² /r

where v is linear velocity

Relation between linear velocity and time period is

so F =

ANSWER:

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2) Given angular velocity rad/s =v/r

coefficient of static friction = 0.25

When coin is moving in a circle the centripetal force is balanced by frictional force

F_c =mg

mv² /r =mg

cancel mass

v²/r =g

v² =g *r ---------------(1)

Divide equation by r²

(v/r)² = g/r

-----------(1)

a) ANSWER = 24.8 cm

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b) Coin is placed at 4.7 cm =0.047 m

Find

Use equation (1)

rad/s

rad/s

ANSWER: rad/s

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