A 5-kg block is launched up a rough ramp with initial speed v0 = 4.5m/s at the b

Question

A 5-kg block is launched up a rough ramp with initial speed v0 = 4.5m/s at the bottom of the ramp. When it reaches the top of the ramp the final speed is vf = 2.69m/s. Choose the bottom of the ramp as zero height.

What is the block's initial gravitational potential energy (GPEi) when it is launched?
What is the block's initial mechanical energy (Ei) when it is launched?
What is the block's final gravitational potential energy (GPEf) when it reaches the top of the ramp?
What is the block's final mechanical energy (Ef) when it reaches the top of the ramp?
Compare the initial and final mechanical energies (Ei and Ef). Calculate the change in mechanical energy, Ef - Ei = (KEf +GPEf) - (KEi + GPEi).
Why do you think Ei and Ef are NOT equal? (Mechanical energy is NOT conserved.)

Explanation / Answer

given,

mass = 5 kg

initial velocity vo = 4.5 m/s

final velocity vf = 2.69 m/s

initial height = 0 m

initial gravitational potential energy = mg * initial height

initial gravitational potential energy = mg * 0

initial gravitational potential energy = 0 J

block's initial mechanical energy = initial kinetic energy + initial potential energy

block's initial mechanical energy = 0.5 * 5 * 4.5^2 + 0

block's initial mechanical energy = 50.625 J

final height = 0.52 m

final gravitational potential energy = 5 * 9.8 * 0.52

final gravitational potential energy = 25.48 J

block's final mechanical energy = 50.625 J because energy is conserved

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