(Non/)Equlibrium and Newton's Laws of Motion

In summary, the conversation discusses a problem involving a crate sliding down a ramp with a given angle and coefficient of kinetic friction. The main issue is the absence of mass in the equation, but it is determined that mass does not affect the solution. The net force equation is set up and simplified to solve for acceleration.
  • #1
Gannon
73
0
This is mainly stumping me because of the absence of any force or mass.

Homework Statement



A crate is sliding down a ramp that is inclined at an angle of 33.6° above the horizontal. The coefficient of kinetic friction between the crate and the ramp surface is 0.485. Find the acceleration of the moving crate.

[tex]\mu[/tex][tex]_{k}[/tex]= .425
[tex]\theta[/tex] = 33.6
g = 9.8m/s[tex]^{2}[/tex]

Homework Equations



Well, F[tex]_{net}[/tex]x = ma , but there is no mass... I don't know where to go from here. :frown:

Any help is appreciated. Thanks.
 
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  • #2
If you think about the ideal concepts of this type of motion, you can see that mass does not matter. Start to solve the equation as if you had a mass (just use 'm' in place of the unknown quantity) and you'll see it's not as important as you think. If you get stuck in the actual solving, post again with your progress.

Bryan
 
  • #3
Ok... I think I'm on the right track. So the net force will be simply

mgsin[tex]\theta[/tex] - [tex]\mu[/tex]mgcos[tex]\theta[/tex] = ma

You can divide everything by mass, leaving

gsin[tex]\theta[/tex] - [tex]\mu[/tex]gcos[tex]\theta[/tex] = a.

Is this correct?
 

1. What is the difference between equilibrium and non-equilibrium?

Equilibrium refers to a state in which all forces acting on an object are balanced, resulting in no net acceleration. Non-equilibrium, on the other hand, refers to a state in which there is a net force acting on an object, causing it to accelerate.

2. How do Newton's Laws of Motion apply to equilibrium and non-equilibrium situations?

Newton's First Law states that an object in motion will remain in motion at a constant velocity unless acted upon by an external force. In an equilibrium situation, this means that the object will continue to remain at rest or in motion with a constant velocity. In a non-equilibrium situation, an external force will cause the object to accelerate according to Newton's Second Law, which states that the net force acting on an object is equal to its mass times its acceleration.

3. What is the relationship between force and acceleration in Newton's Second Law?

Newton's Second Law states that the net force acting on an object is equal to its mass times its acceleration. This means that the greater the force acting on an object, the greater its acceleration will be, and vice versa. This relationship allows us to calculate either force or acceleration if the other is known.

4. Can an object be in equilibrium and still be moving?

Yes, an object can be in equilibrium while still moving at a constant velocity. This is known as dynamic equilibrium. An example of this is a car driving at a constant speed on a flat road. The forces acting on the car, such as the force of friction and the force of gravity, are balanced, resulting in no net force and therefore no acceleration. However, the car is still in motion.

5. How does the concept of inertia relate to Newton's First Law?

Inertia is the tendency of an object to resist changes in its state of motion. This relates to Newton's First Law, which states that an object in motion will remain in motion unless acted upon by an external force. In other words, an object's inertia causes it to resist changes in its motion, and an external force is needed to overcome this inertia and cause acceleration.

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