An 89 N box of oranges is being pushed across a horizontal floor. As it moves, it is slowing at a constant rate of 1.20 m/s each second. The push force has a horizontal component of 25 N and a vertical component of 30 N downward. Calculate the coefficient of kinetic friction between the box and floor.
Fb = 89 N. @ 0 deg. = Force of box.
Fp = 89*sin(0) = 0 = Force parallel to
the floor.
Fv = 89*cos(0) = 89 N. = Force perpendicular to the floor.
mg = 89,
m=89/g = 89/9.8 = 9.08 kg=Mass of box.
Fn = Fap-Fp-Fk = ma,
25-0-Fk = 9.08*-1.2 = -10.9,
-Fk = -10.9-25 = -35.9,
Fk = 35.9 N. = Force of kinetic friction.
u(89+30) = 35.9
119u = 35.9,
u = 0.30 = Coefficient of kinetic friction.
To calculate the coefficient of kinetic friction between the box and the floor, we need to first find the net force acting on the box.
In this case, the only horizontal force acting on the box is the push force, which has a horizontal component of 25 N. The vertical component of the push force (30 N downward) does not affect the horizontal motion of the box.
However, there is another force acting on the box, the force of kinetic friction. This force opposes the motion of the box, causing it to slow down. We can calculate the force of kinetic friction using Newton's second law:
F_net = m * a
Here, F_net is the net force on the box, m is the mass of the box, and a is the acceleration of the box.
Given that the box is slowing down at a constant rate of 1.20 m/s each second, the acceleration is -1.20 m/s² (negative because it is slowing down). The mass of the box is not given directly, but since we have the weight of the box (89 N), we can use the equation:
Weight (W) = mass (m) * gravity (g)
Given that the weight of the box is 89 N and the acceleration due to gravity is approximately 9.8 m/s², we can solve for the mass of the box:
m = W / g = 89 N / 9.8 m/s² ≈ 9.08 kg
Now, we can plug these values into Newton's second law to find the net force acting on the box:
F_net = m * a = 9.08 kg * -1.20 m/s² ≈ -10.896 N
Since the force of kinetic friction is the only horizontal force acting on the box, it must be equal to the net force:
F_friction = -10.896 N
Now, we can calculate the coefficient of kinetic friction (μ) using the equation:
F_friction = μ * N
Here, N is the normal force, which is equal to the weight of the box (89 N) because the box is on a horizontal surface. Rearranging the equation, we get:
μ = F_friction / N = -10.896 N / 89 N
Calculating this, we find:
μ ≈ -0.1224
Now, it is important to note that the coefficient of kinetic friction cannot be negative. Negative sign in this case indicates the direction of the force of friction is opposite to the direction of motion (slowing down). Hence, to get the correct value of μ, we take the magnitude of the calculated value:
μ ≈ 0.1224
Therefore, the coefficient of kinetic friction between the box and the floor is approximately 0.1224.