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 2.2 J 3.4 J 6.0 J
To calculate the gravitational potential energy of the pendulum at the point of release, we can use the formula:
Gravitational Potential Energy (PE) = mass (m) x acceleration due to gravity (g) x height (h)
Given:
Length of the pendulum (h) = 1.2 m
Mass of the pendulum (m) = 0.8 kg
Angle raised to (θ) = 50 degrees
To find the height (h), we can use the equation:
h = L(1 - cosθ), where L is the length of the pendulum
h = 1.2(1 - cos(50))
h ≈ 1.2(1 - 0.6428)
h ≈ 1.2(0.3572)
h ≈ 0.4286 m
Now, we can calculate the gravitational potential energy using the formula mentioned earlier:
PE = mgh
PE = (0.8 kg)(9.8 m/s^2)(0.4286 m)
PE = 3.34 J
Therefore, the gravitational potential energy of the pendulum at the point of release is approximately 3.34 J. Hence, the closest option is 3.4 J.