A ball with a mass of 4·kg is moving in a vertical circle at the end of a 0.9·m long rope. When the ball is at the top of the circle, it is going 7·m/s. What is the tension in the rope? (Again...don't need the answer...just the formula on how to find tension...already understand net force and centripetal acceleration...any help)??
Tension + Weight provides the centripetal force at the top of the loop.
T + M g = M V^2/R
T = M (V^2/R - g)
To find the tension in the rope, we need to consider the forces acting on the ball at the top of the circle.
In this case, there are two forces acting on the ball: the gravitational force (mg) and the tension force (T) in the rope. The net force on the ball is the centripetal force, which is directed towards the center of the circular motion and is given by (mv^2)/r, where m is the mass of the ball, v is its velocity, and r is the radius of the circle (which is the length of the rope in this case).
At the top of the circle, the net force acting on the ball is the difference between the gravitational force and the tension force:
Net force = mg - T
Since the ball is at the top of the circle, its velocity is directed towards the center, so the net force is equal to the centripetal force:
Net force = (mv^2)/r
Setting these two equations equal to each other, we have:
mg - T = (mv^2)/r
Now we can solve for the tension force (T):
T = mg - (mv^2)/r
Plugging in the given values:
Mass of the ball, m = 4 kg
Velocity of the ball, v = 7 m/s
Radius of the circular motion, r = 0.9 m
T = (4 kg)(9.8 m/s^2) - (4 kg)((7 m/s)^2)/(0.9 m)
Simplifying this equation will give you the tension in the rope.