If the 2kg pendulum ball is lifted to 1.5 m above its lowest point, what will its velocity be when it falls back down to its lowest point?

Apply conservation of energy; the pendulum's maximum potential energy (at the highest point of its motion) equals the maximum kinetic energy (at the lowest point of its motion):

Max PE = Max KE

We will calculate the max PE, ie the potential energy after that ball is lifted up:

Max PE = mgh

PE is the potential energy, m is the ball's mass, g is acceleration due to earth's gravity, and h is the height.

Given values:

m = 2kg

g = 9.81m/s²

h = 1.5m

Plug in the values and solve for Max PE:

Max PE = 2(9.81)(1.5)

Max PE = 29.43J

The ball's kinetic energy is given by:

KE = 0.5mv²

We know the ball's velocity is greatest when it attains Max KE, and the max KE equals the Max PE:

Max KE = Max PE = 29.43J = 0.5mv²

Given values:

m = 2kg

Now plug in and solve for v:

2v² = 58.86

v = 5.425

v = 5.4m/s

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