How Does a Ball's Velocity and Acceleration Change on a Circular Path?

[x86]

Homework Statement

A ball moving in the circular path with a constant speed of 3.0 m/s changes direction by 40.0 degrees in 1.75 seconds. What is the change in velocity? What is the acceleration during the time?

Homework Equations

Fc = m * ac
ac = v^2/r

The Attempt at a Solution

No clue to be honest, the velocity shouldn't change, because of the acceleration. And we don't know the radius, so I'm not sure how to solve this at all

 

[tms]

No clue to be honest, the velocity shouldn't change, because of the acceleration. And we don't know the radius, so I'm not sure how to solve this at all

Remember that velocity is a vector, with both a magnitude and a direction. If the direction changes, then there is acceleration.

 

[x86]

Remember that velocity is a vector, with both a magnitude and a direction. If the direction changes, then there is acceleration.

Right, the only thing i can see is 40 degrees / 1.75 seconds.

Okay, so the acceleration has to be 3 m/s^2 every time it changes direction... So if the direction changes everyone 1 second for the velocity to be 3 m/s the acceleration would have to be 3 m/s^2. I'm getting closer, I think

WAIT! I think I did it.

Period.

T = (360 degrees) / ((40 degrees) / (1.75 s)) = 15.75 s

D = vt

2pir = v * 15.75 s

r = 3.0 m/s * 15.75 s / (2 pi) = 7.52007106 meters

ac = v^2 / r = 9.0 m^2/s^2 / 7.52 m =1.19680851 m / s^2 = 1.2 m/s^2

Now, to figure out velocity

1.2 m/s^2 * t = v

The final velocity = 1.2 m/s^2 * 1.75 s = 2 m/s

But it wants the change in velocity. I'm not sure what this means? What is change in velocity?

 

[tms]

Right, the only thing i can see is 40 degrees / 1.75 seconds.

That is the angular speed. You also have the translational speed. Find a relation between those two quantities (that will give you $r$).

Okay, so the acceleration has to be 3 m/s^2 every time it changes direction...

An object in uniform circular motion is always changing direction.

 

[x86]

That is the angular speed. You also have the translational speed. Find a relation between those two quantities (that will give you $r$).

An object in uniform circular motion is always changing direction.

Yes, I made an attempt at the solution and I think its right. But, what do they mean by change in velocity? I have no idea what this could mean.

The final velocity is 2.0 m/s. But the change would be something I'm not sure of. They could mean delta V, but then again that would give me an answer of 1.0 m/s, and the book says the answer is 2.0 m/s. But the book confirms the acceleration is correct.

EDIT: nevermind. i get it now.

The change in direction accounts for the change in velocity. Therefore, 1.2 m/s^2 * 1.75 seconds (time its changing) = 2.1 m/s which is the answer.

Thank you for those tips by the way, they helped me solve the problem. I totally forgot about period and such

 

[tms]

But, what do they mean by change in velocity?

Change in velocity is just the definition of acceleration. It does sound a bit like a trick question, asking for the same thing twice using different words.

Thank you for those tips by the way, they helped me solve the problem. I totally forgot about period and such

You're welcome.