A frictionless pendulum has a length of 1.2 m and a mass of 0.8 kg. If the pendulum is raised to an angle of 50 degrees before it is released, then what is the pendulum’s gravitational potential energy at the point of release?(1 point) Responses 0.34 J 0.34 J 2.2 J 2.2 J 3.4 J 3.4 J 6.0 J
The gravitational potential energy of a pendulum is given by the equation:
PE = mgh
Where m is the mass, g is the acceleration due to gravity, and h is the height.
In this case, the mass of the pendulum is 0.8 kg and the height is given by the vertical distance from the point of release to the lowest point of the pendulum's swing, which is given by:
h = L(1 - cosθ)
Where L is the length of the pendulum and θ is the angle.
Plugging in the values, we have:
h = 1.2(1 - cos50°) = 1.2(1 - 0.6428) = 0.55776 m
Now, we can calculate the potential energy:
PE = (0.8 kg)(9.8 m/s^2)(0.55776 m) ≈ 4.34 J
Therefore, the correct answer is 4.34 J.