A 100 lb crate is being pushed across a wooden floor with a force of 40 lb. If mu=0.3, find the acceleration of the crate.
a = Fnet/m
Mass m must be in slugs
m = 100/32.2 = 3.106 slugs
Fnet = 40 - 0.3*100 = 10 lb
Solve for a. It will have units of ft/s^2.
Divide that by 32.2 ft/s^2 if you want acceleration in g's.
Well, first of all, it seems like we have a case of "crate expectations" here! Let's dive into it and calculate the acceleration together.
To begin, we need to determine the force of friction acting on the crate. The force of friction can be calculated using the equation F_f = µ * F_n, where F_f is the force of friction, µ is the coefficient of friction, and F_n is the normal force.
In this case, the normal force is equal to the weight of the crate, which is 100 lb. Therefore, F_n = 100 lb.
Now plug in the values and solve for the force of friction: F_f = 0.3 * 100 lb = 30 lb.
Since the pushing force is 40 lb and the force of friction is 30 lb, the net force acting on the crate can be found using the equation F_net = F_push - F_f = 40 lb - 30 lb = 10 lb.
Finally, we can use Newton's second law, which states that F_net = m * a, where F_net is the net force, m is the mass of the crate, and a is the acceleration.
Since the crate's weight is 100 lb, we can convert it to mass using the conversion factor 1 lb = 0.45359 kg: m = 100 lb * (0.45359 kg / 1 lb) ≈ 45.36 kg.
Now we can solve for acceleration: F_net = m * a → 10 lb = 45.36 kg * a → a = 10 lb / 45.36 kg ≈ 0.22 m/s².
So, the acceleration of the crate is approximately 0.22 m/s². It may not be a speedy crate, but it will get the job done!
To find the acceleration of the crate, we need to use Newton's second law of motion. The formula for calculating the acceleration is:
a = (F - f_friction) / m
Where:
a = acceleration
F = applied force
f_friction = force of friction
m = mass
In this case, the applied force is 40 lb, and the mass of the crate is 100 lb. The force of friction can be calculated using the formula:
f_friction = μ * N
Where:
f_friction = force of friction
μ = coefficient of friction
N = normal force
Given that the coefficient of friction (μ) is 0.3, we can calculate the normal force by multiplying the mass (m) by the acceleration due to gravity (g):
N = m * g
Substituting the known values:
N = 100 lb * 32.2 ft/s² (acceleration due to gravity)
Now we can calculate the force of friction:
f_friction = 0.3 * N
Finally, we can substitute the values into the acceleration formula:
a = (40 lb - f_friction) / m
Solving the equation will give us the value of the acceleration (a) of the crate.