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

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 = (Fcos25^(\circ) - \mu_(s)Fsin25^(\circ))/(\mu_(s)* g)`

`m = (750cos25^(\circ) - 750sin25^(\circ))/(0.61* 9.8) = 81.36\ kg`