Problem involving centripetal force of a circle

  • Thread starter pokeefer
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  • #1
pokeefer
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Homework Statement



Here is a diagram:
http://i55.tinypic.com/k18g14.jpg

A ball of mass 0.75 kg on the end of a cord is swung in a circle of radius 1.5 m with a period of 1.5 s as shown in the diagram.

a.) What is the speed of the ball?

b.) What is the acceleration of the ball?

c.) What centripetal force must be exerted by the cord to keep the ball in orbit?

d.) What is the mass of the central object? (Hint: Use Pythagoras' theorem to calculate the force of tension in the string.)

e.) What angle does the cord make with the vertical?

f.) How long is the cord, L?

Homework Equations



Velocity = 2(pie)r / T (T = period in seconds)

Acceleration centripetal = v^2 / r
Force centripetal = mv^2 / r

The Attempt at a Solution



I know all parts except for d, e and f


a.) velocity of ball is 6.28 m/s

b.) centripetal acceleration of ball is 26.3 m/s^2

c.) centripetal force of ball is 19.7 N

d.) ??

e.) ?

f.) ?

Thanks
 

Answers and Replies

  • #2
Delphi51
Homework Helper
3,407
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The force of gravity on the hanging central weight provides the tension force in the string to the ball. This includes both the centripetal force and the upward force necessary to counteract gravity on the ball.
spinning.jpg

The ball is not accelerating vertically, so the upward component of T equals the mg down. The tension in the string and thus the weight of the hanging weight can be calculated from the known mg and Fc. Careful with the angle - question asks for angle with vertical, so likely something larger than 45 degrees.
 

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