Newtons second law/friction problem

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In summary, the minimum force magnitude required to start the crate moving is 344.7N, but the answer in the book is 300N. The force of the rope has two components, one in the x-direction and one in the y-direction. By accounting for the angle of inclination (15 degrees), we can find the components of the force and solve for the unknown magnitude.
  • #1
renob
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Homework Statement


A 68 kg crate is dragged across a floor by pulling on a rope attached to the crate and inclined 15 degrees above the horizontal.

(a) If the coefficient of static friction is .50, what minimum force magnitude is required from the rope to start the crate moving?
(b) If [tex]\mu[/tex]k=0.35, what is the magnitude of the initial acceleration of the crate?

Homework Equations


F=ma

The Attempt at a Solution


part a:

I calculated the weight (9.8)(68 kg)=666N

then I got static friction: (666N)(.50)=333N

I substituted all the forces into Newtons second law and got:
ma=Normal+Gravity+Static+Applied force

after I plugged in the variables I got 0=333N + (force applied)(cosx)
(It's 0 because the box isn't moving so a=0)

when i solve for force i get 344.7N but the answer in the book is 300N
 
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  • #2
The Force of the rope has 2 components.

The Y component is lightning the load of the 666 N by F*Sinθ . And it's F*Cosθ that is the force applied in the X direction to move it.

Try looking at what happens then if you account for that with θ = 15.
 
  • #3
The force is unknown though. How can I find the components of the force if the magnitude is an unknown?
 
  • #4
renob said:
The force is unknown though. How can I find the components of the force if the magnitude is an unknown?

But F is your only unknown.

Write out your equation and solve for F.

You know the components of F from θ = 15.
 
  • #5
the original equation I had was 333N=Fcosx

would it be 333N=Fcosx + Fsinx?

sorry I'm very confused.
 
  • #6
wait I see it now. thanks
 

Related to Newtons second law/friction problem

What is Newton's Second Law?

Newton's Second Law of Motion states that the force acting on an object is equal to its mass times its acceleration. In other words, the greater the mass of an object, the more force is needed to accelerate it, and the greater the acceleration, the more force is needed to achieve it.

What is the formula for Newton's Second Law?

The formula for Newton's Second Law is F=ma, where F is the force in Newtons, m is the mass in kilograms, and a is the acceleration in meters per second squared.

How does Newton's Second Law relate to friction?

Friction is a force that opposes motion and is caused by the interaction between two surfaces. According to Newton's Second Law, the force of friction (Ff) is equal to the coefficient of friction (μ) multiplied by the normal force (Fn). This can be written as Ff = μFn.

What is the coefficient of friction?

The coefficient of friction is a number that represents the amount of friction between two surfaces. It is a unitless value and is dependent on the materials and surfaces in contact. A higher coefficient of friction means more force is needed to overcome the friction and move the object.

How can Newton's Second Law and friction be applied in real-life situations?

Newton's Second Law and friction are essential concepts in understanding and predicting the movement of objects in everyday situations. For example, they can be used to calculate the force needed to move a heavy object, the stopping distance of a vehicle, or the speed of an object sliding down a ramp. They are also crucial in engineering and designing structures, machines, and vehicles.

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