A 2 kg rock is released from rest at a height of 20 m. Ignore air resistance and determine the kinetic energy, gravitational potential energy, and total mechanical energy at each of the following heights: 20, 10, and 0 m.

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A 2 kg rock is released from rest at a height of 20 m. Ignore air resistance and determine the kinetic energy, gravitational potential energy, and total mechanical energy at each of the following heights: 20, 10, and 0 m.

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agaue agaue · Answer 1 · 2025-03-25T23:33:02-04:00

At 20 m kinetic energy is 0 J, Potential energy is 392.4 J and total energy is 392.4 J

At 10 m kinetic energy is 196 J, Potential energy is 196.2 J and total energy is 392.4 J

At 0 m kinetic energy is 392.4 J, Potential energy is 0 J and total energy is 392.4 J

Explanation:

Kinetic energy = 0.5 x Mass x Velocity²

KE = 0.5mv²

Potential energy = Mass x Acceleration due to gravity x Height

PE=mgh

Here m = 2 kg

g = 9.81 m/s²

Substituting

KE = 0.5 x 2 x v² = v²

PE= 2 x 9.81 x h = 19.62h

At height 20 m:-

v = 0 m/s

h = 20 m

Substituting

KE = v² = 0² = 0J

PE= 19.62 x 20 = 392.4 J

Total energy = 0 + 392.4 = 392.4 J

At 20 m kinetic energy is 0 J, Potential energy is 392.4 J and total energy is 392.4 J

At height 10 m:-

We have equation of motion v²=u²+2as

v = ?

u = 0 m/s

s = 20 - 10 = 10 m

a = 9.81 m/s²

v²=0²+2 x 9.81 x 10

v = 14 m/s

h = 10 m

Substituting

KE = v² = 14² = 196 J

PE= 19.62 x 10 = 196.2 J

Total energy = 196 + 196.2 = 392.4 J

At 10 m kinetic energy is 196 J, Potential energy is 196.2 J and total energy is 392.4 J

At height 0 m:-

We have equation of motion v²=u²+2as

v = ?

u = 0 m/s

s = 20 - 0 = 20 m

a = 9.81 m/s²

v²=0²+2 x 9.81 x 20

v = 19.81 m/s

h = 0 m

Substituting

KE = v² = 19.81² = 392.4 J

PE= 19.62 x 0 = 0 J

Total energy = 392.4 + 0 = 392.4 J

At 0 m kinetic energy is 392.4 J, Potential energy is 0 J and total energy is 392.4 J