Answer to Question #190586 in Classical Mechanics for Manu

Question

A box, of mass 8 kg, is on a rough horizontal surface.

A string attached to the box is used to pull it along the surface.

The string is inclined at an angle of 40° above the horizontal.

The tension in the string is 50 newtons.

As the box moves a distance of x metres, its speed increases from 2ms1 to 5ms-1

The coefficient of friction between the box and the surface is 0.4

By using an energy method, find x.

Answer 1

$\Delta E=A,$

$\frac{m(v_2^2-v_1^2)}{2}=(T\cos \alpha -\mu mg)x,$

$x=\frac{m(v_2^2-v_1^2)}{2(T\cos \alpha -\mu mg)}=12~m.$