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## Main Question or Discussion Point

today my dynamics lecturer illustrated a situation to us where energy did not appear to be conserved.

The situation involves observing the motion of a mass sliding down a slope, height 'h' above the ground from rest

initially in the rest frame, we see;

initially,

PE = mgh

KE = 0

as the mass starts from rest (we are assuming the force required to start the motion of the mass is insignificant)

and finally (at the bottom of the slope),

PE = 0

KE = 1/2 mv^2

NB. i cannot work out how to make a diagram and post it, but imagine the mass is sliding down the slope to the right.

using this we can claculate the simple equation to determine the final velocity of the mass (to the right)

v = (2gh)^(1/2)

This was simple to comprehend, but now our lecturer asked us to imagine observing the motion from another inertial frame moving to the right (relative to the rest frame) at velocity, v = (2gh)^(1/2)

when drawing this, we see the mass now appears to initially be be moving to the left with velovity, v = (2gh)^(1/2), and when the mass reaches its maximum velocity (v = (2gh)^(1/2) to the right) at the bottom, the mass appears to be at rest.

thus when observing from this frame we see the following occuring

initially

PE = mgh

KE = 1/2 mv^2 = mgh

hence, initial energy, E=2mgh

and finally (at the bottom of the slope)

PE = 0

KE = 0

this obviously seems to disagree with the conservation of energy and im sure there is something wrong with what i have described, but i simply do not know

can anyone explain what is really going on here...?

The situation involves observing the motion of a mass sliding down a slope, height 'h' above the ground from rest

initially in the rest frame, we see;

initially,

PE = mgh

KE = 0

as the mass starts from rest (we are assuming the force required to start the motion of the mass is insignificant)

and finally (at the bottom of the slope),

PE = 0

KE = 1/2 mv^2

NB. i cannot work out how to make a diagram and post it, but imagine the mass is sliding down the slope to the right.

using this we can claculate the simple equation to determine the final velocity of the mass (to the right)

v = (2gh)^(1/2)

This was simple to comprehend, but now our lecturer asked us to imagine observing the motion from another inertial frame moving to the right (relative to the rest frame) at velocity, v = (2gh)^(1/2)

when drawing this, we see the mass now appears to initially be be moving to the left with velovity, v = (2gh)^(1/2), and when the mass reaches its maximum velocity (v = (2gh)^(1/2) to the right) at the bottom, the mass appears to be at rest.

thus when observing from this frame we see the following occuring

initially

PE = mgh

KE = 1/2 mv^2 = mgh

hence, initial energy, E=2mgh

and finally (at the bottom of the slope)

PE = 0

KE = 0

this obviously seems to disagree with the conservation of energy and im sure there is something wrong with what i have described, but i simply do not know

can anyone explain what is really going on here...?