Crate on a conveyor belt..?
A 11 kg crate is placed on a horizontal conveyor belt. The materials are such that u s = 0.55 and u k =0.26. What is the maximum acceleration the belt can have without the crate slipping? How would you draw a free body diagram of the forces acting on the crate (what would it look like?) I know that gravity pulls downward on the crate, but which direction is the normal in, and friction?
Forces on crate: friction on the belt causes acceleration.
mu*mg=ma
solve for a
I wouldn't draw the weight, as it is countered by the converyor holding it up, so it is net zero. What is important is net force accelerating, or friction.
To determine the maximum acceleration without the crate slipping, we need to consider the forces acting on the crate.
First, let's draw a free body diagram to visualize these forces:
1. Start by drawing a rectangle to represent the crate.
2. Draw an arrow pointing downwards to represent the force of gravity pulling the crate downwards. Label it as mg, where m is the mass of the crate (11 kg) and g is the acceleration due to gravity (9.8 m/s^2).
3. Next, draw a perpendicular arrow pointing upwards from the surface of the crate. This represents the normal force, which is the force exerted by the conveyor belt to support the weight of the crate. Label it as N.
4. Finally, draw an arrow parallel to the surface of the crate, pointing in the opposite direction of motion. This represents the force of friction. Label it as f.
The normal force (N) acts perpendicular to the surface of the crate and conveyor belt, in an upward direction. This force counterbalances the downward force of gravity and prevents the crate from sinking into the conveyor belt.
The force of friction (f) opposes the motion of the crate and acts parallel to the surface of the crate. In this case, since the crate is not slipping, the force of friction is at its maximum value, given by f = u_s * N, where u_s is the coefficient of static friction and N is the normal force.
Now that we know the forces acting on the crate, the maximum acceleration the belt can have without the crate slipping can be determined. We can use the equation of motion along the horizontal direction:
f = m * a
Where f is the force of friction, m is the mass of the crate, and a is the acceleration.
Substituting the maximum value of friction (f = u_s * N) into the equation:
u_s * N = m * a
Since N = mg, we can rewrite the equation as:
u_s * mg = m * a
Simplifying and solving for a, we get:
a = (u_s * g)
Substituting the given values (u_s = 0.55 and g = 9.8 m/s^2) into the equation:
a = (0.55 * 9.8)
a = 5.39 m/s^2
Therefore, the maximum acceleration the belt can have without the crate slipping is 5.39 m/s^2.