A pendulum is 0.50 m long and the bob has a mass of 1.0 kg. At the bottom of its swing, the bob's speed is 1.6 m/s.
What is the tension in the string at the bottom of the swing?
Tbottom=((v2/r)+g)
To find the tension in the string at the bottom of the swing, we need to use the concept of centripetal force.
The centripetal force acting on an object moving in a circular path is given by the formula:
F = (m * v^2) / r
Where:
F is the centripetal force
m is the mass of the object
v is the velocity of the object
r is the radius or length of the string in this case.
In this scenario, the tension in the string at the bottom of the swing provides the centripetal force that keeps the bob moving in a circular path.
Given:
m = 1.0 kg (mass of the bob)
v = 1.6 m/s (velocity of the bob at the bottom of the swing)
r = 0.50 m (length of the string)
Let's substitute these values into the formula:
F = (1.0 kg * (1.6 m/s)^2) / 0.50 m
F = (1.0 kg * 2.56 m^2/s^2) / 0.50 m
F = 2.56 kg⋅m/s^2 / 0.50 m
F = 5.12 N
Therefore, the tension in the string at the bottom of the swing is 5.12 N.