Question

Ciara is swinging a 0.015 kg ball tied to a string around her head in a flat, horizontal circle. The radius of the circle is 0.70 m. The ball is going 7.33 m/s.

If the speed is tripled, what happens to its centripetal force?
a)The new centripetal force is 1/3 what it was
b)The new centripetal force is 9 times more
c)The new centripetal force is 1/9 what it was
d)The new centripetal force is 3 times more

Answer 1

b)The new centripetal force is 9 times more

Step-by-step explanation:

The formula to apply in this case is that of tension force on a spring which is equal to the centripetal force.

T= mv²/r --------i

where T is the tension on the spring

v= velocity/speed of the ball = 7.33 m/s

m= mass of the ball , 0.015 kg

r= radius of circle , 0.70 m

Use the values in the formula as;

T= {0.015 * 7.33² } / 0.70

T= 0.8059335 / 0.70

T= 1.15 N ---------i

If the speed is tripled then;

v= 21.99 m/s

T= 0.015 * 21.99² / 0.70

T= 10.36 N ------ii

Check the changes by dividing i and ii as ;

10.36 / 1.15 = 9.01

This is 9 times more hence if the speed is tripled ,the new centripetal force is 9 times more.