A crate of mass 42kg moving with a speed of 8m-1 on a rough horizontal floor is brought to rest after sliding a distance of 5m on the floor.calculate the coefficient of sliding friction between the crate and the floor
Calculate the coefficient of sliding friction between the crate and the floor
F = m*g = 42 * 9.8 = 411.6 N. = force of crate = normal force(Fn).
Fp = F*sin A = 411.6*sin 0 = 0 = Force parallel with plane.
V^2 = Vo^2 + 2a*d = 0.
8^2 + 2a*5 = 0,
a = -6.4 m/s^2.
Fp - u*Fn = M*a.
0 - u*411.6 = 42 * (-6.4),
u = 0.653. = Coefficient of friction.
To calculate the coefficient of sliding friction between the crate and the floor, you can use the formula:
μ = (m*g*d) / (m*(v^2)/2)
where:
μ = coefficient of sliding friction
m = mass of the crate (42 kg)
g = acceleration due to gravity (approximately 9.8 m/s^2)
d = distance slid on the floor (5 m)
v = initial velocity of the crate (8 m/s)
Let's plug in the given values and calculate:
μ = (42 kg * 9.8 m/s^2 * 5 m) / (42 kg * (8 m/s)^2 / 2)
First, calculate the numerator:
Numerator = 42 kg * 9.8 m/s^2 * 5 m = 2058 kg * m/s^2
Now, calculate the denominator:
Denominator = 42 kg * (8 m/s)^2 / 2
= 42 kg * 64 m^2/s^2 / 2
= 42 kg * 32 m^2/s^2
= 1344 kg * m^2/s^2
Now, divide the numerator by the denominator:
μ = 2058 kg * m/s^2 / 1344 kg * m^2/s^2
Canceling out the units, we get:
μ = 2058 / 1344
Now, divide 2058 by 1344 to get the coefficient of sliding friction, μ:
μ ≈ 1.5327
Therefore, the coefficient of sliding friction between the crate and the floor is approximately 1.5327.