Circular Motion Homework: Radial & Tangential Accel, Total Accel

[blackboy]

Homework Statement

A ball tied to the end of a string .5m in length swings in a vertical circle under the influence ofgravity. When the string makes an angle of 20 with the vertical, the ball has a speed of 1.5 m/s. Find the magnitude of radial and tangential acceleration at this instant. Then find the total acceleration.

Homework Equations

Circular Motion Ones

The Attempt at a Solution

I know Radial, but Tangential has always troubled me. The tangential is the derivative of the velocity vector. The answer says the tangential acceleration=gsin20. Can someone explain that to me? Thanks!

 

[LowlyPion]

Make a drawing.

The 20° is with the vertical. That means that the direction tangent to the circle it describes is also at 20°. Draw that out and verify.

That makes it just like it's subject to acceleration from gravity in the same way that it would if it was sliding down an incline doesn't it? (Only at that point however.)

 

[blackboy]

I drew it out. I can't see the relationship between g and a though. I drew it out and saw 2 vectors a and g, which is along the vertical. I moved the a vector up along the radius, until it touched the vertical. Then I saw that it was gsin20, but I think what I did was not legit. If you can, can you draw it out for me?

 

[LowlyPion]

I drew it out. I can't see the relationship between g and a though. I drew it out and saw 2 vectors a and g, which is along the vertical. I moved the a vector up along the radius, until it touched the vertical. Then I saw that it was gsin20, but I think what I did was not legit. If you can, can you draw it out for me?

Can't draw it for you.

But all you need to do is draw a tangent to the circle and extend it until it crosses the vertical. Since angle between the radius and the vertical is 20°, the slope of that line relative to the horizontal must necessarily also be 20°.

 

[blackboy]

Ok I get it now. But what does the other leg represent?

Make a drawing.


That makes it just like it's subject to acceleration from gravity in the same way that it would if it was sliding down an incline doesn't it? (Only at that point however.)

Why is it only at that point?

 

[LowlyPion]

Ok I get it now. But what does the other leg represent?

Why is it only at that point?

Don't know that it represents anything, except that the angle that gravity acts through is what you need to know.

The ball is tethered, and hence constrained to describe a circular path. As soon as it moves a Δθ then the sineθ becomes sine(θ +Δθ).

 

[blackboy]

But if we stop it another time, it still is subject to acceleration from gravity right?

 

[LowlyPion]

But if we stop it another time, it still is subject to acceleration from gravity right?

As long as it is moving in the vertical plane it is of interest. When you have motion in the horizontal plane, the force is normal to motion and of less interest.

 

[blackboy]

Yeah the problem stated it was moving in a vertical circle. Thanks for all your help!