A 2kg ball is attached to a 1.5m rope and is swung in a vertical circle. At the top of the swing the ball travels at 5 m/s. What is the tension in the rope?
To find the tension in the rope, we need to analyze the forces acting on the ball at the top of the swing.
1. Start by calculating the gravitational force acting on the ball. The gravitational force is given by the formula F_gravity = m * g, where m is the mass of the ball (2 kg) and g is the acceleration due to gravity (approximately 9.8 m/s^2). So, F_gravity = 2 kg * 9.8 m/s^2 = 19.6 N.
2. At the top of the swing, the tension in the rope provides the centripetal force needed to keep the ball moving in a circle. The centripetal force is given by the formula F_centripetal = (m * v^2) / r, where v is the velocity of the ball (5 m/s) and r is the radius (1.5 m).
3. Substitute the values into the formula: F_centripetal = (2 kg * (5 m/s)^2) / 1.5 m = 33.33 N.
4. The tension in the rope is equal to the sum of the gravitational force and the centripetal force, because the ball is not accelerating horizontally at the top of the swing. So the tension in the rope is: Tension = F_gravity + F_centripetal = 19.6 N + 33.33 N = 52.93 N.
Therefore, the tension in the rope is approximately 52.93 N.