A 3 kg ball is traveling in a circle of radius 2 meters with a tangential velocity of 2 meters/second. Find the centripetal acceleration of the ball and the centripetal force acting on it.
To find the centripetal acceleration of the ball, we can use the formula:
a = v^2 / r
where:
a = centripetal acceleration
v = tangential velocity
r = radius of the circle
From the given information, we have:
v = 2 meters/second
r = 2 meters
Substituting these values into the formula, we get:
a = (2 meters/second)^2 / 2 meters
Simplifying the equation, we have:
a = 4 meters^2/second^2 / 2 meters = 4/2 meters/second^2 = 2 meters/second^2
So, the centripetal acceleration of the ball is 2 meters/second^2.
To find the centripetal force acting on the ball, we can use the formula:
F = ma
where:
F = centripetal force
m = mass of the ball
a = centripetal acceleration
From the given information, we have:
m = 3 kg
a = 2 meters/second^2
Substituting these values into the formula, we get:
F = 3 kg * 2 meters/second^2
Simplifying the equation, we have:
F = 6 kg * meters/second^2
So, the centripetal force acting on the ball is 6 Newtons.