A balling ball of mass 70.2 kilogram is attached to the ceiling by a 4.20 meter rope. The ball is pulled to to one side and set to horizontal circular motion with a speed of 3.6 meters per second. The angle between the rope and the vertical axis is 30 degrees when pulled.Tension of the rope is calculated using which formula?
To calculate the tension of the rope in this scenario, we can use the centripetal force formula. In circular motion, an object moving in a circle experiences a force directed towards the center of the circle, which is known as the centripetal force. In this case, the tension in the rope provides the centripetal force that keeps the ball moving in a circle.
The formula for centripetal force is:
F = (mv^2) / r
Where:
F = Centripetal force
m = Mass of the object (in this case, the bowling ball with a mass of 70.2 kg)
v = Velocity of the object (3.6 m/s in this case)
r = Radius of the circular motion (the length of the rope, which is 4.20 meters)
Plugging in the values, the formula becomes:
F = (70.2 kg * (3.6 m/s)^2) / 4.20 m
After calculating the expression on the right side, the result will be the tension in the rope in newtons (N).