A frictionless pendulum with a mass of 1.2 kg is released from point A, which is at a height of h = 0.4 m. What is the speed of the pendulum as it passes through point C? (1 point) Responses 2.8 m/s 2.8 m/s 7.8 m/s 7.8 m/s 4.7 m/s 4.7 m/s 2.0 m/s 2.0 m/s
To find the speed of the pendulum as it passes through point C, we can use the principle of conservation of mechanical energy.
The total mechanical energy of the pendulum is the sum of its potential energy (PE) and kinetic energy (KE).
At point A, the pendulum has only potential energy, given by the equation PE = mgh, where m is the mass (1.2 kg), g is the acceleration due to gravity (9.8 m/s^2), and h is the height (0.4 m). So, at point A, the potential energy is PE = (1.2 kg)(9.8 m/s^2)(0.4 m) = 4.704 J.
At point C, the pendulum has only kinetic energy, given by the equation KE = (1/2)mv^2, where m is the mass (1.2 kg) and v is the speed we want to find. Since there is no friction, the total mechanical energy at point C is equal to the mechanical energy at point A, so KE = PE. Therefore, (1/2)(1.2 kg)v^2 = 4.704 J.
Solving for v, we have v^2 = (2(4.704 J))/(1.2 kg) = 7.8 m^2/s^2.
Taking the square root of both sides, we get v = √(7.8) ≈ 2.8 m/s.
Therefore, the speed of the pendulum as it passes through point C is approximately 2.8 m/s.
The correct response is: 2.8 m/s