Question

A sled is being pulled across a horizontal patch of snow. Friction is negligible. The pulling force points in the same direction as the sled's displacement, which is along the +x axis. As a result, the kinetic energy of the sled increases by 36.8 percent. By what percentage would the sled's kinetic energy have increased if this force had pointed 66.3 ° above the +x axis?

Answer 1

We apply the kinetic energy theorem

For the first case we write

$0.368 \cdot \Delta E_k=F \cdot S$ (1)

For the second case we write

$x \cdot \Delta E_k=F \cdot S \cdot \cos(66.3^0)$ (2)

divide the first equation into the second

$\frac{}{}$ $\frac{0.368 \cdot \Delta E_k}{x \cdot \Delta E_k}=\frac{F \cdot S }{F \cdot S \cdot \cos(66.3^0)}$

reduce these terms we get the ratio

$\frac{0.368 }{x}=\frac{1 }{cos(66.3^0)}$

Then the desired value is equal to (Increase in kinetic energy in the second case)

$x=0.368 \cdot \cos(66.3^0)=0.368 \cdot 0.402=0.148=14.8{\%}$