A 35.4 kg crate is at rest on a level floor, and the coefficient of kinetic friction is 0.323. The acceleration of gravity is 9.8 m/s^2. If the crate is pushed horizontally with a force of 186.012 N, how far does it move in 5.11 s? Answer in units of m.
To find the distance the crate moves in 5.11 seconds, we can use the equation of motion:
d = v₀t + (1/2)at²
Where:
d is the distance
v₀ is the initial velocity (0 m/s, since the crate is at rest)
t is the time (5.11 s)
a is the acceleration
To find the acceleration, we need to calculate the net force acting on the crate. The net force is the force applied minus the force of friction. The force of friction can be calculated using the formula:
f_friction = μ * N
Where:
μ is the coefficient of kinetic friction (0.323)
N is the normal force, which is equal to the weight of the crate (mass * gravity).
First, let's calculate the weight of the crate:
Weight = mass * gravity
Weight = 35.4 kg * 9.8 m/s²
Now, we can calculate the force of friction:
f_friction = μ * weight
Next, we can calculate the net force:
Net Force = applied force - force of friction
Finally, we can calculate the acceleration:
a = Net Force / mass
Now that we have the acceleration, we can substitute it into the equation of motion to find the distance:
d = (1/2) * a * t²
Let's calculate the distance step by step.