# Velocity of a ball at the highest point using the radius

• lanzjohn
In summary: I read the problem again and looked at the figure.In summary, the ball will swing along the dashed arc at a speed of 4.47124 m/s.
lanzjohn

## Homework Statement

The string in the Figure is L = 102.0 cm long and the distance d to the fixed peg P is 73.4 cm. When the ball is released from rest in the position shown, it will swing along the dashed arc.How fast will it be going when it reaches the highest point in its swing?

## Homework Equations

PE: mg(2r)
KE: (1/2)*mv^2

mg(2r)+(1/2)*mv^2= C (Total E)

## The Attempt at a Solution

Having troubles. The M's do not cancel out in this one soo I am all flustered. Is it just alegbra now? But my question is what is C? How can the M's cancel out so that I can begin to compute V. I mean I found the velocity at the lowest point of the arc which was 4.47124 m/s. So I guess with knowing velocity I can figure out mass but when I tried that I was still a little confused.

Energy is conserved. Write the energy for the initial position of the ball to get the total energy.

ehild

How would I write it for initial position?

I thought I wrote it for total E?
mg(2r)+(1/2)*mv^2

The total energy is the same at every position of the ball, 1/2 mv2 + mgh (h is the height with respect to the lowest position). Look at the initial position before the ball is released and stationary yet. What is the potential energy?

ehild

So your saying to find the highest point, which is in the circle I should do:

(1/2)mv^2 = mg(2r)

(1/2)v^2 = g(2r)

V = sqrt ((g(2r))/.5)?

lanzjohn said:
So your saying to find the highest point, which is in the circle I should do:

(1/2)mv^2 = mg(2r)

(1/2)v^2 = g(2r)

V = sqrt ((g(2r))/.5)?

And no that is incorrect. So I take it that is not at all what you said.

Well how can I find PE if I don't know mass?

lanzjohn said:
And no that is incorrect. So I take it that is not at all what you said.

Yes, what you did was wrong. But you did not do what I have said. Hint: read the problem again and look at the figure.

ehild

## 1. What is the formula for calculating the velocity of a ball at the highest point using the radius?

The formula for calculating the velocity of a ball at the highest point using the radius is v = √(rg), where v is the velocity, r is the radius, and g is the acceleration due to gravity.

## 2. How does the radius of the ball affect its velocity at the highest point?

The radius of the ball does not directly affect its velocity at the highest point. However, it does affect its acceleration due to gravity, which in turn affects its velocity at the highest point. A larger radius will result in a greater acceleration due to gravity, and therefore a higher velocity at the highest point.

## 3. Can the velocity of a ball at the highest point be greater than its initial velocity?

No, the velocity of a ball at the highest point cannot be greater than its initial velocity. According to the laws of physics, the velocity at the highest point will always be equal to the initial velocity at the moment of release.

## 4. Does air resistance affect the velocity of a ball at the highest point?

Yes, air resistance can affect the velocity of a ball at the highest point. If there is significant air resistance, the ball may not reach its maximum height and therefore its velocity at the highest point will be lower than expected. However, if the air resistance is negligible, then it will not have a significant effect on the velocity at the highest point.

## 5. How does the angle of release affect the velocity of a ball at the highest point?

The angle of release does not directly affect the velocity of a ball at the highest point. However, it does affect the trajectory and the maximum height the ball can reach. A higher angle of release will result in a higher maximum height and therefore a higher velocity at the highest point. On the other hand, a lower angle of release will result in a lower maximum height and a lower velocity at the highest point.

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