Question

You push downward on a box at an angle 25° below the horizontal with a force of 750 N. If the box is on a flat horizontal surface for which the coefficient of static friction with the box is 0.61, what is the mass of the heaviest box you will be able to move?

Answer 1

Answer:

The heaviest box that can be moved will have a mass of 81.36 kg

Solution:

As per the question:

Angle, $\theta = 25^{\circ}$

Force, F = 750 N

Static Friction Coefficient, $\mu_{s} = 0.61$

Now,

The acceleration of the box is zero.

The net force, $F_{net}$ that acts on the box is zero, thus:

$Fcos25^{\circ} = \mu_{s}mg + \mu_{s}Fsin25^{\circ}$

$m = \frac{Fcos25^{\circ} - \mu_{s}Fsin25^{\circ}}{\mu_{s}\times g}$

$m = \frac{750cos25^{\circ} - 750sin25^{\circ}}{0.61\times 9.8} = 81.36\ kg$