Question

Which form of the law of conservation of energy describes the motion of the block when it slides from the top of the table to the bottom of the ramp?

Answer 1

By definition we have that the energy at the top of the ramp is equal to the energy at the bottom of the ramp. This is due to the principle of energy conservation.

We have then:

$E1 = E2$

The energy at the top is only potential energy:

$E1 = mgh$

Where,

• m: mass
• g: acceleration of gravity
• h: vertical height of the ramp

The energy when it falls is transformed into kinetic energy and therefore:

$E2 = \frac {1} {2} mv ^ 2$

Where,

• v: object speed.

Therefore we have:

$mgh = \frac {1} {2} mv ^ 2$

Answer:

The potential energy is transformed into kinetic energy.

$mgh = \frac {1} {2} mv ^ 2$