A box of books weighing 290 N is shoved across the floor of an apartment by a force of 400 N exerted downward at an angle of 34.9° below the horizontal. If the coefficient of kinetic friction between box and floor is 0.57, how long does it take to move the box 3.80 m, starting from rest?

1.95s

Explanation:

Given

ma = 290 cos 34.9 - fk

fk = 290 cos 34.9 - ma

fn = mg + 400 sin Φ

fn = 290 + 400 sin 34.9

fn = 290 + 228.9

fn = 518.9

fk = fn * uk

uk = 0.57

290 cos 34.9 - ma = 518.9 * 0.57

290 cos 34.9 - ma = 295.8

290 cos 34.9 - 295.8 = ma

ma = -58

m = 290/10 = 29

a = 58/29

a = 2

Using equation of motion

S = ut + .5at²

3.8 = 0 + .5*2*t²

3.8 = t²

t = 1.95s

increase masses, decrease separation