Question

Consider a uniform gravitational field (a fair approximation near the surface of a planet). Find U(yf)−U(y0)=−∫yfy0F⃗ g⋅ds⃗ , where F⃗ g=−mgj^ and ds⃗ =dyj^.

Answer 1

Answer:

U(yf) − U(y0) = mg( yo - yf )

Step-by-step explanation:

We have that

$U(y_f)-U(y_o)=-\int_{y_f}^{y_o}\textbf{F}_g\cdot d\textbf{s}\\\textbf{F}_g=mg\hat{j}\\d\testbf{s}=dy\hat{j}$

Hence we have

$F_g \cdot ds =-mgdy$

and by replacing in the integral we have

$-\int_{y_f}^{y_o}(-mgdy)=mg[y_o-y_f]$

hope this helps!