A box of books weighing 349 N moves with
a constant velocity across the floor when it is
pushed with a force of 434 N exerted downward
at an angle of 37.9◦ below the horizontal.
Find μk between the box and the floor.
To find the coefficient of kinetic friction (μk) between the box and the floor, we can use the equation:
μk = Ff / Fn
where Ff is the force of friction and Fn is the normal force.
First, let's find the normal force (Fn) acting on the box. In this case, since the box is not accelerating vertically, the vertical forces must be balanced:
Fn - Fg = 0
where Fg is the force of gravity acting on the box. The force of gravity (weight) can be calculated using the formula:
Fg = m * g
where m is the mass of the box and g is the acceleration due to gravity (approximately 9.8 m/s^2).
Given that the weight of the box is 349 N, we can solve for the mass (m) using the formula:
m = Fg / g
Next, we need to determine the force of friction (Ff) acting on the box. The force of friction can be calculated using the formula:
Ff = μk * Fn
Now we can substitute the values we have and solve for μk:
Fn = Fg = m * g
Ff = 434 N
Fn = m * g
By substituting Fn and Ff into the equation for μk, we get:
μk = Ff / Fn
μk = (434 N) / (m * g)
With the given information, we can now calculate μk.