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 0.66, what is the mass of the heaviest box you will be able to move?

Answer 1

72.75 kg

Step-by-step explanation:

`F` = force applied on a box = 750 N

`m` = mass of the box

`N` = Normal force on the box

`\mu _(s)` = Coefficient of static friction = 0.66

From the force diagram, force equation along the vertical direction is given as

`N = F Sin25 + mg`

`N = 750 Sin25 + mg` eq-1

Static frictional force is given as

`f_(s) = \mu _(s) N`

using eq-1

`f_(s) = \mu _(s) (750 Sin25 + mg)`

For the box to move,

`F Cos25 = f_(s)`

`750 Cos25 = \mu _(s) (750 Sin25 + mg)`

`750 Cos25 = (0.66) (750 Sin25 + m (9.8))`

m = 72.75 kg