Question

A 0.5 kg mass moves 40 centimeters up the incline shown in the figure below. The vertical height of the incline is 7 centimeters. What is the change in the potential energy (in Joules) of the mass as it goes up the incline?

Answer 1

Answer:

The change in potential energy of the mass as it goes up the incline is 0.343 joules.

Explanation:

We must remember in this case that change in the potential energy is entirely represented by the change in the gravitational potential energy. From Work-Energy Theorem and definition of work we get that:

$U_{g}= m\cdot g\cdot \Delta y$

Where:

$U_{g}$ - Gravitational potential energy, measured in Joules.

$m$ - Mass, measured in kilograms.

$g$ - Gravitational acceleration, measured in meters per square second.

$\Delta y$ - Change in vertical height, measured in meters.

This work is the energy needed to counteract effects of gravity at given vertical displacement.

If we know that $m = 0.5\,kg$, $g = 9.807\,\frac{m}{s^{2}}$ and $\Delta y = 0.07\,m$, the change in the potential energy of the mass as it goes up the incline is:

$U_{g} = (0.5\,kg)\cdot \left(9.807\,\frac{m}{s^{2}} \right)\cdot (0.07\,m)$

$U_{g} = 0.343\,J$

The change in potential energy of the mass as it goes up the incline is 0.343 joules.