# From what height did the lead ball fall without initial velocity if its temperature increased by DT = 10 K during the fall?

**From what height did the lead ball fall without initial velocity if its temperature increased by DT = 10 K during the fall? Consider that 80% of the ball’s energy went into heating it. Neglect air resistance. Specific heat of lead c = 130 J / (kg * K)**

When a lead ball moves, it has potential and kinetic energies. When the ball is at a height of 10 meters, it has potential energy, and its kinetic energy will be zero, since in the problem statement it is said that the ball moves without initial velocity.

Potential energy:

П = m * g * h, where

m – body weight

h – the height from which the ball falls

g we take equal to 10

80% of the potential energy went to heating the ball, which means we get the following equality:

0.8 * m * g * h = c * m * t

we reduce the masses:

0.8 * g * h = c * t

h = (c * t) / (0.8 * g)

h = (130 * 10) / (0.8 * 10) = 162.5 m

Answer: the ball fell from a height of 162.5 meters