Question

10. A 10-kg box starting from rest is pulled using a rope that makes an angle of 30o with the horizontal. If it travels a distance of 10 km in 2s, what is the magnitude of the force exerted by the rope? 

Answer 1

Find the acceleration:

$$a=\frac{2d}{t^2}.$$

Assuming zero friction, find the force that creates this acceleration along the horizontal:

$$F_x=ma=\frac{2md}{t^2}.$$

Find the magnitude of the force that, projected on the x-axis, gives F_x:

$$F=\frac{F_x}{\cos\theta}=\frac{2md}{t^2\cos\theta},\\\space\\ F=\frac{2·10·10000}{2^2\cos30°}=57735\text{ N}.$$