A ball on the end of a string is revolving at a uniform rate in a vertical circle of radius 92.5 cm. If its speed is 4.50 m/s, and its mass is 0.335 kg, calculate the tension (in newtons) in the string when the ball is at the bottom of the path.
To find the tension in the string when the ball is at the bottom of the path, we can consider the forces acting on the ball at that point. At the bottom of the path, the ball experiences two main forces: the tension force pulling the ball inward and the gravitational force pulling the ball downward.
The tension force provides the centripetal force required to keep the ball moving in a circular path. The centripetal force is given by the equation:
F_c = (m * v^2) / r,
where F_c is the centripetal force, m is the mass of the ball, v is the speed of the ball, and r is the radius of the circle.
Plugging in the given values, we get:
F_c = (0.335 kg * (4.50 m/s)^2) / 0.925 m.
Calculating this expression gives us the centripetal force.
Now, at the bottom of the path, the ball also experiences the gravitational force pulling it downward. The gravitational force is given by:
F_g = m * g,
where F_g is the gravitational force and g is the acceleration due to gravity.
Plugging in the given mass and the standard value of acceleration due to gravity (9.8 m/s^2), we can calculate the gravitational force.
Now, at the bottom of the path, the total tension force in the string will be the sum of the centripetal force and the gravitational force. Therefore, we can calculate the tension in the string by adding these forces together.
T = F_c + F_g.
Substituting the previously calculated values, we can find the tension in the string when the ball is at the bottom of the path.