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Matter In Our Surroundings

Question
CBSEENSC9006291

An object of mass 40 kg is raised to a height of 5 m above the ground. What is its potential energy ? If the object is allowed to fall, find its kinetic energy when it is half-way down. 

Solution
Given space that comma space

Mass space of space the space body comma space straight m space equals space 40 space kg

Acceleration space due space to space gravity comma space space straight g space equals space 10 space ms to the power of negative 2 end exponent

Height space from space which space the space object space is space falling comma space space straight h space equals space 5 space straight m

Potential space energy space of space the space object space at space straight a space height space of space 5 space straight m comma

space space space space space space space space space space space space space space space straight E subscript straight p space equals space mgh space equals space 40 space cross times space 10 space cross times space 5 space equals space 2000 space straight J.

When space the space object space is space half minus way space down space left parenthesis straight s space equals space 2.5 space straight m right parenthesis comma space let space its space velocity space be space straight v.

Then comma
space space space space space space space space space space space space space space space space straight v squared space minus space straight u squared space equals space 2 gs
space space space space space space space space space space space space space space space space space straight v squared space minus 0 squared space equals space 2 cross times 10 space cross times 2.5 space
rightwards double arrow space space space space space space space space space space space space space straight v squared space equals space 50

therefore space space space space space Kinetic space energy space of space the space object comma

space straight E subscript straight K equals 1 half mv squared space equals space 1 half cross times 40 cross times 50 space equals space 1000 space straight J.