Answer :
To find the tension in the string when the ball is at the bottom of the path, sum the gravitational force (1.7836 N) and the centripetal force (2.731 N), resulting in a tension of approximately 4.515 N.
Explanation:
To calculate the tension in the string when the ball is at the bottom of the path, we need to consider the forces acting on the ball. These include the gravitational force (weight of the ball) and the force needed to provide centripetal acceleration to keep the ball moving in a circle. The tension in the string is the sum of these two forces when the ball is at the bottom of its path.
The gravitational force is calculated using the formula Fg = m × g, where m is the mass (0.182 kg) and g is the acceleration due to gravity (9.8 m/s2). The centripetal force required to keep the ball moving in a circle is given by Fc = (m × v2) / r, where v is the velocity (3.74 m/s) and r is the radius of the circle (0.977 m).
Calculating each force:
Gravitational Force, Fg = 0.182 kg × 9.8 m/s2 = 1.7836 N
Centripetal Force, Fc = (0.182 kg × (3.74 m/s)2) / 0.977 m = 2.731 N
Summing these forces when the ball is at the bottom of its path gives us the tension in the string:
Tension (T) = Fg + Fc = 1.7836 N + 2.731 N = 4.5146 N
Therefore, the tension in the string when the ball is at the bottom of the path is approximately 4.515 N.