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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.)

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whitneytr12

Answer:

[tex]F_{c}=m\frac{v^{2}}{L}[/tex]

Step-by-step explanation:

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

[tex]F_{c}=ma_{c}[/tex]

Now, the [tex]a_{c}=\frac{v^{2}}{R}[/tex]

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

Therefore, the centripetal force will be:

[tex]F_{c}=m\frac{v^{2}}{L}[/tex]

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

I hope it helps you!

facundo3141592

The centripetal force is the mass of the ball times the centripetal acceleration, so we get:

F = m*v^2/L

How to get the centripetal force?

By Newton's second equation, we know that:

F = m*a

Force equals mass times acceleration.

Particularly, the centripetal force will be the mass of the ball times the centripetal acceleration, and the centripetal acceleration is given by:

a = v^2/L

Where v is the tangential velocity and L is the radius of the circle (the length of the string).

Then the centripetal force is:

F = m*v^2/L

Notice that this is a radially inwards force, so if you use polar notation, the sign should be negative.

If you want to learn more about forces, you can read:

https://brainly.com/question/20905151

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