Question

A 30kg girl initially at rest is pushed by a force, F of 23 N that parallel to an inclined plane, the girl slides down along 4m on frictionless inclined plane. Determine the
a) energy and speed of the girl at the bottom of the slide.
b) speed of the girl at the bottom of the slide if no force is being applied to the girl.

Answer 1

Assume that the inclined plane form an angle of 30 ° with the horizon

$a)$

$mg\sin\alpha+F=ma\to a=g\sin\alpha+F/a=$

$=9.8\cdot\sin30°+23/30=5.7(m/s^2)$

$v=\sqrt{2aS}=\sqrt{2\cdot5.7\cdot4}=6.8(m/s)$

$E=\frac{mv^2}{2}=\frac{30\cdot6.8^2}{2}=684(J)$

b)

$mg\sin \alpha=ma\to a=g\sin\alpha=9.8\cdot \sin 30°=4.9(m/s^2)$

$v=\sqrt{2aS}=\sqrt{2\cdot4.9\cdot4}=6.3(m/s)$