Question

Show that work and energy are dimensionally equal

Answer 1

Answer:

KINETIC ENERGY

Work = (force)(distance)

∴

W=(−F)(S)

note that F is negative since it is opposite the direction of motion (pointing to the left)

but F=ma

∴

W=(−ma)(S)

but Newton’s equation of motion says V2f−V2i=2aS

but Vf=0

∴

−V2i=2aS

or

a=−V22S

∴

W=(−m)(−V22S)(S)

or

W=12mV2

POTENTIAL ENERGY

PE=mgh

After lifting the object to this height, it now has the potential to do work equal to:

work = (force)(distance)

or

work = (weight)(distance)

or

work = (mg)(h)

Thus it now has potential energy = mgh

PLZ FOLLOW ME

Explanation:

Answer 2

Answer:

KINETIC ENERGY

Work = (force)(distance)

∴

W=(−F)(S)

note that F is negative since it is opposite the direction of motion (pointing to the left)

but F=ma

∴

W=(−ma)(S)

but Newton’s equation of motion says V2f−V2i=2aS

but Vf=0

∴

−V2i=2aS

or

a=−V22S

∴

W=(−m)(−V22S)(S)

or

W=12mV2

POTENTIAL ENERGY

PE=mgh

After lifting the object to this height, it now has the potential to do work equal to:

work = (force)(distance)

or

work = (weight)(distance)

or

work = (mg)(h)

Thus it now has potential energy = mgh

PLZ FOLLOW ME

Explanation: