# Velocity & Energy Homework: Find Speed at Low/High Points

• TS656577
In summary, the conversation discusses a string attached to a ball that is fixed at one end and has a fixed peg at a certain distance. The question asks for the speed of the ball at its lowest and highest points after being released horizontally. The attempt at a solution involves using the conservation of energy equation and solving for the velocity by plugging in the given values. However, the answer obtained is incorrect according to the online program.
TS656577

## Homework Statement

The string in Fig. 8-37 is L = 129 cm long, has a ball attached to one end, and is fixed at its other end. The distance d from the fixed end to a fixed peg at point P is 78 cm. When the initially stationary ball is released with the string horizontal as shown, it will swing along the dashed arc. What is its speed when it reaches (a) its lowest point and (b) its highest point after the string catches on the peg?

## Homework Equations

K=1/2mv^2
U=mgh where in this case, h=L

## The Attempt at a Solution

I know I need to use the conservation of energy (U(i) + K(i) = U(f) + K(f)) and then K(i)=0 and U(f)=0. So then you can use the equation mgL = 1/2mv^2 and the m's cancel out so youre left with gL = 1/2v^2. I took this to mean that I would have 9.8(129) = 1/2v^2. Solving for v, I got 50.28 m/s. The online program says that's wrong so I'm at a loss.

#### Attachments

• fig08_38.gif
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I'm still at a loss for this one

Your approach using the conservation of energy is correct. However, the equation for potential energy should be U=mgh where h is the vertical height from the lowest point to the highest point, not just the length of the string (L).

So, for the lowest point, h=L-d, and for the highest point, h=L+d.

Plugging these values into the equation and solving for v, you should get v=15.54 m/s for the lowest point and v=34.46 m/s for the highest point.

It's important to remember that the potential energy at the highest point is equal to the kinetic energy at the lowest point, so the speeds should be different.

Hope this helps!

## 1. What is velocity?

Velocity is a measure of the rate at which an object changes its position. It is a vector quantity, meaning it has both magnitude (speed) and direction.

## 2. How is velocity different from speed?

Velocity takes into account the direction of an object's motion, whereas speed only measures the rate of change in position. For example, a car traveling at 50 miles per hour east has a different velocity than a car traveling at 50 miles per hour west.

## 3. How do you calculate velocity?

Velocity is calculated by dividing the change in an object's position by the time it took to make that change. The formula for velocity is v = Δx/Δt, where v is velocity, Δx is change in position, and Δt is change in time.

## 4. What is the relationship between velocity and energy?

Velocity and energy are related because an object's velocity affects its kinetic energy. The faster an object is moving, the higher its kinetic energy will be. Kinetic energy is defined as 1/2 mv^2, where m is an object's mass and v is its velocity.

## 5. How can I find the speed at low and high points?

To find the speed at low and high points, you will need to use the formula for velocity (v = Δx/Δt). The low and high points can be represented as two positions, and the time it takes to travel between those points is the change in time. Plug these values into the formula to calculate the velocity at those points. Remember to use the correct units for distance and time (e.g. meters and seconds).

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