I need help with this Physics problem?

Question

A swing carousel consists of rotating circular platform 11m in diameter from which 10 kg seats are suspended at the end of 2.57m massless chains. When the system rotates the chains make an angle of 17.2 degrees with the vertical.

1)what is the speed of each seat? (Answer in units of m/s)
2)If a child of mass 28.8 kg sits in a seat, what is the tension in the chain for the same angle? (answer in units of Newton)

Answer 1

Use the force, Luke.

Seriously--It's usually easiest to attack such problems by analyzing the forces.

I'll get you started. If you actually want to understand how to work the problem, read this answer. If you're looking to cheat on your homework, read other peoples' answers.

Forces acting on a given seat:
1. gravity, downward (amount: mg (don't know how much "m" is, but don't worry about it).
2. Tension of chain, pulling upward and "inward". Amount: T (don't know yet how much that is, but that's what variables are for).

Now think about the seat's acceleration. It is moving in a horizontal circle. So you can use the formula a = v²/r for the acceleration. ("r" is given in the problem. "v" is something you don't know yet.

Acceleration is a vector: so what's its direction? For things moving in a circle at constant speed, the direction of acceleration is _always_ toward the center of the circle. In this case, this means the acceleration is a horizontal-pointing vector.

Aha! This means the net force must also be horizontal and pointing toward the center of the circle. This is a clue.

Now let's look at the forces again. Take the diagonal force (the tension T) and break it into horizontal and vertical components (hint: this will involve sin(17.2) and cos(17.2)). That makes it easier to work with below.

Now, since we know the NET force is horizontal, that means the _vertical_ components of the force must cancel out. That should be enough to let you write an equation relating the downward weight (mg) to the upward (vertical) component of the tension. Write that equation now.

Now write an equation for the horizontal (centripetal) force:

Fc = ???

(hint: the right side will have "T" and "17.2" in it.)

So now let's look at the acceleration again. Previously we expressed it in terms of v and r; but this time we'll express it in terms of Newton's law F=ma. That gives us:

a = Fc/m

Okay, so the equations you wrote previously (analyzing the forces) already have some "Fc"'s and some "m"'s in them. So that should allow you to rewrite the above equation in some different terms:

a = Fc/m = ????

(hint: the "????" part will have a "g" and a "17.2" in it)

ALMOST DONE. Now take the equation for "a" that you just wrote, and equate that to the _previous_ equation for "a" that you wrote (that is: a = v²/r)

Now you should have an equation that's got "v", "r", "g" and "17.2" in it. You already know "g"; the problem gives you "r"; so you should be able to solve for "v". That answers question #1.

For question #2, you can refer to one of the equations you already wrote. Looking them over, I'd say your best bet is the one that relates the upward component of "T" to the downward weight. That will let you solve for "T" in terms of "m" (given in the problem) and "g" and "17.2".

Answer 2

the galaxies rotate at speeds inconsistent with their obvious mass is by way of the fact we do see all of it. i'm concerning it as being the theoretical dark remember. There are very sturdy proofs that shows that dark remember exist. One the is the inconsistent velocity of and obvious mass. dark remember makes up approximately seventy 5% to 80% of the undertaking interior the Universe...