Question

The long pendulum shown is drawn aside until the ball has risen 0.5 m. it is then given an initial speed of 3.0 m/s.. the speed of the ball at its lowest position is:

Answer 1

m = mass of the ball being raised

h = height to which the ball is raised = 0.5 m

v₀ = initial speed given to the ball = 3 $\frac{m }{s}$

v = final speed of the ball at its lowest position = ?

using conservation of energy

final kinetic energy at the lowest point  = initial kinetic energy + initial potential energy

(0.5) m v² =  (0.5) m v₀² + mgh

dividing each term by "m"

(0.5) v² =  (0.5) v₀² + gh

inserting the values

(0.5) v² =  (0.5) (3)² + (9.8) (0.5)

v = 4.34 m/s