Samantha pushes a 100 kg crate on a ramp that makes 14.3 degrees with the horizontal. What is the change in potential energy of this crate after Samantha pushes it for 8.50 m along the ramp?

The Work/ Energy principle states that the increase in the body's total energy is equal to the total work done on a body. Mathematically it can be expressed as:

[tex]W_n_e_t=\Delta E=W_a_b =E_b - E_a[/tex]

So, we can find the change in potential energy of this crate finding the work done by it. The work can be calculated as:

[tex]W_a_b=F*s*cos(\theta)[/tex]

Where:

[tex]F=Force\\s=Displacement\\\theta= Angle\hspace{3}between\hspace{3}the\hspace{3}force\hspace{3}and \hspace{3}the\hspace{3}displacement[/tex]

Assuming the gravity of Earth as:

[tex]g=9.8[/tex]

And using the picture I attache you:

The magnitude of the force is given by:

[tex]|F|=\sqrt{(100*9.8*sin(14.3))^2+(100*9.8*cos(14.3))^2} =980[/tex]

Therefore:

[tex]W_a_b = \Delta E = 980*cos(14.3)*8.5=8071.901043J[/tex]