Question

If the speed of the ball at the bottom of the circle is v, what is the expression for the centripetal force on the ball in terms of its speed v and the length L of the string? Take the upward direction as positive and the downward direction as negative when considering the sign of the forces. (Use the following as necessary: m, v and L.)

Answer 1

Answer:

$F_{c}=m\frac{v^{2}}{L}$

Step-by-step explanation:

The centripetal force is product of the mass times the centripetal acceleration

$F_{c}=ma_{c}$

Now, the $a_{c}=\frac{v^{2}}{R}$

• v is the tangential velocity
• R is the radius of the circle (L in our case)

Therefore, the centripetal force will be:

$F_{c}=m\frac{v^{2}}{L}$

It has a positive sign because the centripetal force points toward the center of the circle.

I hope it helps you!