What is the mass of the ball and the tension in the string?

[09jml90]

Homework Statement

In the diagram below, the horizontal force, F, holds the ball steady. Given F = 7.0 N, and $$\theta$$ = 18 deg, calculate the mass of the ball.

I can't get the link to the picture to work, but it looks like a basic free body diagram with a ball. The ball is m, with an arrow, F, protruding from the right of this ball. At about 130-140 deg from the positive x-axis an arrow for, T, points towards a direction that you could imagine as northwest. The string is also hung from this angle, so a thin line that indicates the string and the arrow, T fall right on each other. If you imagine upper section of the string, angle theta which is 18 deg is indicated which is drawn to the left of the string.

What is the tension in the string.

Homework Equations

$$\sum F$$ = ma

I think you do components, not 100% sure.

The Attempt at a Solution

I drew a free body diagram with a coordinate system where T lies directly along the -x-axis. Using Fx = 7.0cos18deg, and Fy = 7.0sin18deg, they were 6.66 N and 2.16 N respectively. But from here, I'm not really sure what to do. In my diagram I also added W = mg.

I also didn't know how to approach the tension problem. Would you need to subtract components?

Thank you

 

[Doc Al]

It might be a bit easier if you stick to a coordinate system using y as the vertical and x as the horizontal.

Hint: The sum of the forces acting on the ball along any direction must be what? Analyze x and y components separately, then combine the equations.

 

[09jml90]

Because the ball is steady with no force giving it an increase in acceleration should all the forces cancel each other out for equilibrium?

 

[Doc Al]

Because the ball is steady with no force giving it an increase in acceleration should all the forces cancel each other out for equilibrium?

Yes: The ball is in equilibrium, the acceleration is zero, so the net force on the ball must be zero.

 

[fizzynoob]

this is basically a statics problem - everything equals zero

Sum the forces in the X, than sum the forces in the Y. You should be able to calculate the mass of the ball using mg found in the Y component of the force.

 

[09jml90]

Ok. Breaking the forces down into components and using the given angle. The x component of tension must equal -7.0 N, and using this I could solve the y component (21.54 N) and ultimately solve the hypotenuse which was the tension. The tension turned out to be 22.65 N. Because it is in equilibrium, all the forces must balance, so because y+ is 21.54 N, in order for everything to balance, the magnitude of the weight must be 21.54 N. With the known value of g, I can solve for mass.

Mass of ball = 2.20 kg
Tension = 22.65 N

 

[09jml90]

Thank you for your help everybody.