A railroad flatcar is loaded with crates. The coefficient of static friction between the crates and the floor is 0.27. If the train is moving at 59.7 km/hr, in how short a distance can the train be stopped with a constant acceleration without causing the crates to slide?
I have noo idea how to do this. Can someone show me the steps?
friction between the crates and floor
Force= mu*mass*g
But that must equal ma, or m (v^2/(2d))
mu*mass*g= mass*v^2/2d and you are looking for d.
How do I find the mass?
A railroad flatcar is loaded with crates. The coefficient of static friction between the crates and the floor is 0.27. If the train is moving at 59.7 km/hr, in how short a distance can the train be stopped with a constant acceleration without causing the crates to slide?
Ok so I understand that mu*mass*g= mass*v^2/2d, and I need to solve for d. But how do I get the mass?
the masses cancel
To determine the shortest stopping distance for the train without causing the crates to slide, we need to find the maximum acceleration the train can have before the crates start sliding. We can relate the acceleration to the coefficient of static friction using the formula:
f = μ * N
where f is the force of friction, μ is the coefficient of static friction, and N is the normal force.
The normal force is equal to the weight of the crates, which can be calculated as:
N = m * g
where m is the mass of the crates and g is the acceleration due to gravity (approximated as 9.8 m/s²).
To find the maximum acceleration, we need to equate the force of friction with the net force acting on the crates, which is equal to the mass of the crates multiplied by the acceleration:
f = m * a
Combining these equations, we can solve for the maximum acceleration:
μ * N = m * a
Substituting the expression for N:
μ * m * g = m * a
Canceling out the mass from both sides:
μ * g = a
Now we can calculate the acceleration:
a = μ * g
In this case, the coefficient of static friction is given as 0.27, and the acceleration due to gravity is 9.8 m/s²:
a = 0.27 * 9.8 m/s²
a = 2.646 m/s²
Now that we have the maximum acceleration, we can determine the stopping distance using the formula:
d = (v² - u²) / (2 * a)
where d is the stopping distance, v is the final velocity (0 m/s as the train has to stop), u is the initial velocity (59.7 km/hr converted to m/s), and a is the acceleration.
Converting the initial velocity:
u = 59.7 km/hr * (1000 m/1 km) * (1 hr/3600 s)
u = 16.583 m/s
Calculating the stopping distance:
d = (0² - 16.583²) / (2 * 2.646 m/s²)
d = (-274.928) / 5.292
d = -51.94 m
The negative sign indicates that the initial velocity is greater than the final velocity, which is expected for a deceleration.
Therefore, the train can be stopped in approximately 51.94 meters without causing the crates to slide.