Dragging an object: what is Fmin and magnitude of acceleration?

In summary, Fmin refers to the minimum force required to overcome static friction and initiate the dragging of an object. The magnitude of acceleration is determined by the net force acting on the object after it has started moving, which is influenced by kinetic friction. The relationship between these forces can be described using Newton's second law, where acceleration increases as the net force exceeds the resistance due to friction.
  • #1
tomiharv
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1
Homework Statement
By pulling a on rope attached to a crate of mass 124.0 kg, the crate is dragged across a floor. Let the coefficient of static friction between the crate and the floor be 0.860 and the angle between the rope and horizontal is 39.6 °. Find the minimum force required to move the crate.
At a later time the crate is now dragged with this same force, and has already started moving, on a wet floor where the kinetic friction coefficient is 0.516. What is the magnitude of the acceleration of the crate?
Relevant Equations
Fn = m*a or m*g (I think this is necessary)
I am not sure how to set this problem up mainly, I am unsure of what equations I need to be using right now. I have tried, for some dumb reason, a multitude of combinations with Cos(39.6) and 124 kg*9.8 m/s^2 as well as one time multiplying the coefficient. I am mainly just struggling with what equations I am meant to be using and believe me I have tried google and I just feel really stupid when I look at this problem so I don't know who else to ask as I feel bad milking my classmates for help with these problem set-ups.

I know that:

124*9.8 (m*g) = 1215.2 N
Cos (39.6) = 0.771 (rounded)
Sin (39.6) = 0.637 (rounded)

So I assume that Normal Force is the 1215.2 N right?

I also know that there's the applied force formula with x-component and y-component (Fa = Fax i + Fay j) would that be necessary for this problem?

I am going to set up a tutor for myself at my school to try and get more into the swing of knowing when to use what equations, there are just so many that I am a bit lost.
 
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  • #2
I suggest starting with a nice free body diagram
 
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  • #3
tomiharv said:
So I assume that Normal Force is the 1215.2 N right?
Wrong. ##mg=1215.2~##N is the weight of the crate. The pulling force has a vertical component away from the floor that lessens the burden of the full weight on the floor.

Follow @Gordianus's hint and draw a nice free body diagram. Then you will be able to see how this is put together.
 
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  • #4
GUYS UPDATE I DID IT I SOLVED IT
 
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FAQ: Dragging an object: what is Fmin and magnitude of acceleration?

What is Fmin in the context of dragging an object?

Fmin refers to the minimum force required to initiate the motion of an object when dragging it across a surface. This force must overcome the static friction between the object and the surface.

How do you calculate Fmin?

Fmin can be calculated using the formula Fmin = μs * N, where μs is the coefficient of static friction between the object and the surface, and N is the normal force, which is typically the weight of the object (mass * gravity) if the surface is horizontal.

What is the magnitude of acceleration when dragging an object?

The magnitude of acceleration (a) can be determined using Newton's second law, which states that F = m * a. Once the object is in motion, the net force applied (after overcoming friction) divided by the mass of the object gives the acceleration. Mathematically, a = (F - Fk) / m, where F is the applied force, Fk is the kinetic friction force, and m is the mass of the object.

How does kinetic friction affect the acceleration of a dragged object?

Kinetic friction (Fk) acts against the motion of the object and reduces the net force available for acceleration. The kinetic friction force can be calculated using Fk = μk * N, where μk is the coefficient of kinetic friction. The net force is then the applied force minus this kinetic friction force.

How do surface properties influence Fmin and acceleration?

Surface properties, such as roughness and material type, influence the coefficients of static and kinetic friction (μs and μk). A rougher or stickier surface will have higher coefficients, requiring a greater Fmin to initiate motion and resulting in greater frictional forces that reduce acceleration. Conversely, smoother surfaces have lower coefficients, making it easier to initiate and maintain motion.

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