Conceptual Understanding: 2nd Law and Coefficient of Friction

In summary, the 1kg object moves at 5m/s right before collision with the 4kg stationary object. After impact, the objects move off in the velocity you calculated (which is 1m/s) and are then decelerated by friction until they come to a full stop. The equation to solve for acceleration is Vf = Vi + at. The solution has this value ma = F of friction = mu*m*g.
  • #1
PhysicsPhil
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Homework Statement



A 1 kg object is moving along at speed of 5 m/s right before colliding with a 4 kg stationary object, in a perfectly inelastic collision.

Suppose that the objects are moving on a surface that has a coefficient of friction of mu=0.2. (Note you may still assume that the first object moves at 5 m/s immediately before collision. After impact, the objects move off in the velocity you calculated (which is 1m/s) and are then decelerated by friction until they come to a full stop


Homework Equations



I'm trying to understand how I can apply Newton's 2nd Law to this. We can solve this by using one of the Kinematics Equations, but we need to calculate acceleration. We know that Vi = 1m/s and that Vf = 0m/s (comes to a stop). But how can we calculate acceleration? I know it has to do with how to calculate the Force of Friction which is equal to mu*N (N is the normal force which is equal to -mg)

The Attempt at a Solution


So here is what the steps of the equation look like

(1) Calculate acceleration
(2) use Vf , Vi, and a to find t through the equation Vf = Vi + at

Then the solution has this

ma = F of friction = mu*m*g

therefore a = mu*g

(mu is Greek Letter meaning coefficient of friction)...

But how is this possible? I tried to think of it in terms of Fnet , but F-net :

Fnet = ma + mu*m*g (Find a from Newton's Second law[i/]

I don't see how "Find a from Newton's Second Law" works here...

But to do what the solutions did we would have to make Fnet = 0 ...

I don't see why we can do this? Is it because we are solving for the distance when it comes to a stop (which is 0 net force?)
 
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  • #2
PhysicsPhil said:
But how is this possible? I tried to think of it in terms of Fnet , but F-net :

Fnet = ma + mu*m*g (Find a from Newton's Second law[i/]

I don't understand the question. There's only one (horizontal) force acting on the body, the friction force. So Fnet = mu*m*g. Newton's 2nd law tells us that Fnet = ma, so mu*m*g = ma, and thus a = mu*g (as you had previously noted).

Can you restate your question?
 
  • #3
Fnet=mu*m*g=ma. Fnet is not zero. The force on the object is constant while it is moving. As you have said, a=mu*g. I'm not sure what it really confusing you. Fnet is only zero if an object is not accelerating.
 
  • #4
I think my confusion came in because I thought there were 2 forces action on the body - as I saw it in my mind's eye - there was a force from 1 the 1kg object that impacted the second object and "pushed" (put a force on it) in the positive x-direction, while it deaccelerated from the Force of Friction acting in the opposite direction.

Maybe I'm just not good at visualizing/seeing these things. Our teacher had told us that, for example, 2 dimension motion, there is never a force acting in the X-direction, so if I apply that same logic here, I see what you are saying - but I just didn't see why there was no force in the direction opposing friction.
 
  • #5
During the collision the objects certainly exert forces on each other! Otherwise the mass at rest would never get moving to begin with. But after the inelastic collision, it's more useful to think of them as one combined object (of mass m1+m2) that is acted upon by friction.
 
  • #6
PhysicsPhil said:
I think my confusion came in because I thought there were 2 forces action on the body - as I saw it in my mind's eye - there was a force from 1 the 1kg object that impacted the second object and "pushed" (put a force on it) in the positive x-direction, while it deaccelerated from the Force of Friction acting in the opposite direction.

Maybe I'm just not good at visualizing/seeing these things. Our teacher had told us that, for example, 2 dimension motion, there is never a force acting in the X-direction, so if I apply that same logic here, I see what you are saying - but I just didn't see why there was no force in the direction opposing friction.

Not an unusual problem. Many students have the impression that if an object is moving in some direction then there must be a force 'pushing' it in that direction. You just have to listen to Newton and get over it.
 

1. What is the second law of thermodynamics?

The second law of thermodynamics states that in any natural process, the total entropy of a closed system will always increase over time. This means that energy tends to spread out and become more disorganized, rather than staying concentrated in one place.

2. How does the second law of thermodynamics relate to the coefficient of friction?

The coefficient of friction is a measure of the resistance between two surfaces that are in contact with each other. The second law of thermodynamics tells us that this resistance will always increase over time, as energy is converted from useful forms to less useful forms like heat. This means that the coefficient of friction will generally increase as a system becomes more disordered and its entropy increases.

3. What factors affect the coefficient of friction?

The coefficient of friction is affected by a variety of factors, including the nature of the surfaces in contact, the amount of force pushing them together, and the presence of any lubricants or other substances between them. It can also be affected by temperature, with some materials becoming more or less slippery as they heat up or cool down.

4. How can we use the coefficient of friction in practical applications?

The coefficient of friction is an important factor to consider in many practical applications, particularly those involving motion and friction. For example, engineers may use it to design more efficient machines or to choose the best materials for a particular task. It is also important in fields like physics and chemistry, where it can help us understand how energy is transferred and transformed in different systems.

5. Do all objects have the same coefficient of friction?

No, the coefficient of friction can vary greatly depending on the materials involved and the conditions under which they are in contact. For example, smooth surfaces tend to have lower coefficients of friction than rough surfaces, and the presence of lubricants can greatly reduce the coefficient of friction. Additionally, the coefficient of friction can change over time as surfaces wear down or as external factors, such as temperature, change.

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