Apendulum of length l=5.0m attached to the ceiling carries a ball of mass 10.0 kg. the ball (a massive bob) is moved from its stationary equilibrium position to some distance such that the pendulum’s rope makes an angle of 60∘∘ with the vertical and then is released and allowed to swing. what is the total energy of the system at the moment of release in joules? assume the lowest point on the trajectory to be y=0. (do not include unit in answer)

    Em₀ = 245 J

Explanation:

We can solve this problem with the concepts of energy conservation, we assume that there is no friction with the air.

Initial energy the highest point

        Em₀ = U

        Em₀ = m g h

The height can be found with trigonometry

The length of the pendulum is L and the length for the angle of 60 ° is L ’, therefore the height from the lowest point is

         h = L - L’

         cos θ = L ’/ L

         L ’= L cos θ

          h = L (1 - cos θ)

We replace

         Em₀ = m g L (1- cos θ)

Let's calculate

         Em₀ = 10 9.8 5.0 (1 - cos 60)

         Em₀ = 245 J

initial speed when it is dropped is 150 ft/s

now at the same moment the acceleration due to gravity is perpendicular to its velocity

so as we know that

now we have centripetal acceleration a = 32 ft/s^2 as its perpendicular to velocity

while tangential acceleration at the same moment will be zero

so

now radius of curvature is given as

so the radius of curvature just after it is dropped is 703.125 ft