Uniform Circular Motion in a Horizontal Plane

[carouselifica]

Hey Guys. I am having issues with one of my physics homework questions, and i was seeking help. The question is as follows:
While traveling around a roundabout, John notices that the fluffy dice suspended from his rear-vision mirror swing out. If John is traveling at 8m/s and the roundabout has a diameter of 5m, what angle will the string connected to the fluffy dice (mass 100g) make with the vertical?

Relevant equations:
V = 2πr/T
T = 1/f
a = v^2/r
a = 4π^2/T^2
F=mV^2/r
F=ma
F=m4π^2r/T

I have attempted this a few times, getting answers of 70* and 20*. We have been told that the answer is 50*, but i can't work out how to do this. I think it has something to do with using trigonometry and the forces to make a triangle, but that is a complete guess, so any help would be amazing!

Thanks for your time.

 

[Doc Al]

Start by drawing a free body diagram of the dice. What forces act on the dice?

 

[gneill]

Hi carouselifica. Welcome to Physics Forums.

5m diameter seems pretty tight for a roundabout. Are you sure its 5m diameter and not 5m radius?

Your hunch about it having to due with trigonometry is correct. There will be two accelerations operating on the fuzzy dice, one being due to gravity. Can you name the other acceleration?

 

[carouselifica]

Hi carouselifica. Welcome to Physics Forums.

5m diameter seems pretty tight for a roundabout. Are you sure its 5m diameter and not 5m radius?

Your hunch about it having to due with trigonometry is correct. There will be two accelerations operating on the fuzzy dice, one being due to gravity. Can you name the other acceleration?

The teacher is wanting to just give us the experience. I was correct in saying it was a 5m diameter. The other force is centripetal force isn't it? I originally thought you would have to find the centripetal force acting on the car, and use the gravity multiplied by the mass to do a vector addition, and then trig, but the answer isn't nearly right, compared to the 50* answer.

 

[Doc Al]

The other force is centripetal force isn't it?

There are two forces acting on the dice: gravity is one, the tension in the string is the other. You need to find the angle that the string--and thus the tension--makes with the vertical.

Draw a free body diagram. What's the ball's acceleration?

Analyze horizontal and vertical force components using Newton's 2nd law.