# physics

A box of books weighing 319 N is shoved across the floor by a force of 485 N exerted downward at an angle of 35 degrees below the horizontal.
a. If 'uk' between the box and the floor is 0.57, how long does it take to move the box 4.00 m, starting from rest?
485sin35= 278 N
485cos35 = 397N
How do I continue?
b. If uk between the box and the floor is 0.75, how long does it take to move the box 4.00 m, starting from rest?

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1. Without the force pushing it, the forces acting on the box are gravity and the opposing force of the floor.
W = 319N downward, = 319N upward exerted by the floor.

Add the pushing force of 485N, downward at 35 degrees, and break it into horizontal and vertical components:
Vertical component = 485 * sin(35) = 278N
Horizontal component = 485 * cos (35) = 397N

With the added force pushing on the box, the downward force is 319N + 278N = 597N
The force exerted by kinetic friction is 597N * .57 = 340N.
The horizontal force is 397N - 340N = 57N

The mass of the box is 319N / 9.81m/s^2 = 32.5 Kg
a = F/m = 57/32.5 = 1.754 m/s^2

d = 1/2 * a * t^2
t = sqrt(2*a/d) = sqrt(3.508/4) = 0.936 seconds.

b) uk = 0.75. F = 597*.75 = 447.75
This is greater than the horizontal component of the applied force, so the box will not move.

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2. how did you get the time? Please explain. Would the downward force be negative?

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