# Horizontal circular motion problem.

1. Nov 16, 2014

### psstudent

1. The problem statement, all variables and given/known data
I have this question to solve for hw : " An object of mass 10 kg is whirled around a horizontal circle of radius 4m" If the uniform speed of the object is 5m/s Calculate a) tension in string b) angle of inclination of string to the vertical.

2. Relevant equations

3. The attempt at a solution
Here is what I tried: I thought of finding the length of the entire string so using 2pi*r I got 25.12. then using the sine inverse of that to get the angle i got 4(radius)/25.12 =.16 sine inverse which would give an angle of 9.2 degrees. then I used tension = mg/cos(theta) = 10 * 9.81/.99 = 99.1 N.

I also tried to work out the angle a different way using k=.5mv2 to find energy which gave me 125 Joules and then i plugged that into the potential energy formula to give me the height so potential energy = mgh thus

h= energy/g*m which gave me 1.27m. then i used CAH trignometry to give me .9 cos inverse = 26degrees. This was the method I used to solve a momentum question but I doubt it works in this case.

Now I realize I made a mistake which is why Im coming here. I thought I had found the length of the string when i used 2pi*r but iI realized I actually just found the perimeter of the circle the radius made. Any help would be appreciated.

2. Nov 16, 2014

### Staff: Mentor

You are given the radius of the horizontal circle of the motion as well as the speed of the mass. You should be able to calculate the centripetal force that is required to keep the given mass moving along that circular path. You should also be able to find the gravitational force acting on that mass. The tension in the rope must provide the force to balance both of those forces. So their Draw a Free Body Diagram for the mass at a given instant, sketching the various force vectors. See if you can't find a relationship between those forces.

3. Nov 16, 2014

### psstudent

Thanks for the reply, but i figured it out. I got the vertical and horizontal components use Pythagorean theorem and then SOH to find the answer