1. Jul 6, 2013

### babysnatcher

A ball tied to the end of a string 0.50 m in length swings in a vertical circle under the influence of gravity. When the string makes an angle x= 20 degrees with the vertical, the ball has a speed of 1.5 m/s. Find the magnitude of the radial component of acceleration at this instant.

So i have a concept question. How do i know that tangential acceleration = gsin(20 degrees).

Basically, prove the general formula tangential acceleration= gsin(x) for this problem.

Last edited: Jul 6, 2013
2. Jul 6, 2013

### WannabeNewton

Draw a free body diagram on the ball at the instant specified in the problem (when it it makes an angle of 20 degrees with the vertical). Then decompose the forces into the radial and tangential directions. That's a good rule of thumb for when you are solving problems using Newton's 2nd law.

3. Jul 6, 2013

### babysnatcher

we havent read about newton's 2nd law yet -- thats the next chapter.

there is already a drawning. i dont see why tangential acceleration=gsin(x)

4. Jul 6, 2013

### WannabeNewton

Well you don't really need it here, I was just saying it's a good rule of thumb in general. But do what I said: draw a free body diagram on the ball; what are the forces acting on the ball at that instant? How can you decompose these forces into radial and tangential directions?

If there's already a diagram, which part of it is troubling you?

5. Jul 6, 2013

### babysnatcher

im not there yet. im on chapter 4, motions in two dimensions. The only force we think of is gravity.

nvm, a teacher helped me with it already. he just moved the radial acceleration vector all the way to the top so that they tip of that vector touches the top of the string. i see the right triangle now.

6. Jul 6, 2013

### voko

We assume that the string cannot change its length. That means that any force applied to the end of the string is effectively cancelled along the string; but its transverse component acts unopposed.

7. Jul 6, 2013

### babysnatcher

I am not thinking about forces in this chapter yet, except for gravity.
hmmm, in g2=at2+y2, what is y2? and what is the physical meaning of this? y doesnt seem to be ar.

I mean pertaining to this triangle at=gsin(x).

Last edited: Jul 6, 2013
8. Jul 6, 2013

### voko

What I wrote fully applies to gravity.

'y' could be the "radial" acceleration if the ball were allowed to fly freely. But it is not, so 'y', and the entire equation for that matter, does not make a lot of sense physically.

What does make sense is $(mg)^2 = (ma_t)^2 + P_r^2$, where $P_r$ is the radial component of the weight.

9. Jul 6, 2013

### babysnatcher

If it does not make sense, then i am still confused about why at=gsin(x).

I havent read about Mass/weight/newtons laws yet so can you explain it with just what I know.

10. Jul 6, 2013

### voko

I did in #6. Just replace "force" with "gravity" there.

11. Jul 6, 2013

### babysnatcher

I still don't get how this makes sense of at=gsin(x). The transverse component of gravity?

12. Jul 6, 2013

### rcgldr

Gravity exerts a force of mg straight down. What is the component of gravity in the direction the ball is traveling when the angle of the string X is 20° from vertical?

13. Jul 6, 2013

### babysnatcher

9.80 m/s2 South. I see a triangle but what is the 3rd side?

14. Jul 6, 2013

### voko

Gravity acting on the ball on a string has the radial and tangential (transverse) components. Find them, that is simple trigonometry.

15. Jul 6, 2013

### babysnatcher

Yes, I get hypotenose g and leg at. I want to know what this other leg is -- I dont understand that.

16. Jul 6, 2013

### voko

You were given an explanation earlier. You rejected it because you did not know some concepts. I am afraid you will have to wait till you know those concepts.

17. Jul 6, 2013

### babysnatcher

Why does Pr not include mass?

18. Jul 6, 2013

### voko

The full equation should be $(mg)^2 = P^2 = P_t^2 + P_r^2$. Tangentially, there is no other force except $P_t$, so we can write $P_t = ma_t$ and then have $(mg)^2 = (ma_t)^2 + P_r^2$. Radially, however, other forces may be present, $ma_r = P_r + F$, so we cannot replace $P_r$ with $ma_r$.

19. Jul 6, 2013

### Staff: Mentor

Were you taught the formula for radial acceleration? V2/R. Note that, in this question, it does not depend on g, since, as stated in the problem description, the ball is traveling in a circle.

20. Jul 6, 2013

### babysnatcher

Im only talking about the tangential acceleration.

I think Pr=mar+F makes more sense because Pr is mar plus other possible forces. Why is it the other way?

Last edited: Jul 6, 2013