Answer to Question #182327 in Physics for Charles

Question

A child is holding a wagon from rolling straight back down a driveway that is inclined at 20°to the horizontal. If the wagon 150N, with what force must the child pull on the handle if the handle is parallel to the incline?. And also repeat this if the handle is now raised at angle of 30° above the incline

Answer 1

Find the force required to pull the wagon at constant velocity for both positions of force F:

a) According to equilibrium of forces:

$$F-mg\sin\theta=0,\\ F=mg\sin\theta=51.3\text{ N}.$$

b) Similarly:

$$F\cos\alpha-mg\sin\theta=0,\\ F=\frac{mg\sin\theta}{\cos\alpha}=59.2\text{ N}.$$