a. At the bottom of the circle, the ball is moving in a circle, so it is experiencing a centripetal acceleration towards the center of the circle. The free body diagram for the ball would show the tension force (T) acting towards the center, and the gravitational force (m*g) acting downwards. The direction of acceleration is towards the center of the circle.
b. Using the free body diagram, we can set up the equation needed to determine the tension in the string:
T = m * a
Where T is the tension in the string, m is the mass of the ball (0.65 kg) and a is the centripetal acceleration of the ball (v^2/r).
c. To calculate the tension in the string, we need to first find the centripetal acceleration. We can use the equation:
a = v^2/r
where v is the velocity of the ball at the bottom of the circle (2.8 m/s) and r is the radius of the circle (0.50 m).
a = (2.8 m/s)^2 / 0.50 m = 11.2 m/s^2
Now, we can use the equation T=m*a to find the tension in the string:
T = 0.65 kg * 11.2 m/s^2 = 7.28 N
So the tension in the string is 7.28 N