# What is the relationship between tension and mass in a system with friction?

• SakuRERE
In summary: There is no difference between the two cases when it comes to the magnitude of the frictional force, which is simply mg*F.
SakuRERE

## Homework Statement

In the figure above a block of mass m is connected to a block of mass M > m by a string. Both blocks sit on a smooth surface with a coefficient of kinetic friction µk between either block and the surface. In figure a), a force of magnitude F (large enough to cause both blocks to slide) is exerted on block M to pull the system to the right. In figure b), a force of (the same) magnitude F is exerted on block m to pull the system to the left. Circle the true statement:
a) The tension Ta > Tb.
b) The tension Ta < Tb.
c) The tension Ta = Tb.
d) There is not enough information to determine the relative tension in the two cases.

known data:
we know that both blocks have the same coefficient of friction and that their masses are different.

ΣF= ma
μk= Fk*N

## The Attempt at a Solution

I drew first the FBD of both block in each situation and wrote the equation. for the first situation (a)
Block M has this equation:
ΣF= ma
F-Ta-Fk=Ma
Ta=F-Fk-Ma
Ta=F-μkMg-Ma
while block m I ended up with:
Ta=ma+μkmg

and for the second situation:
block M equation:
Tb= Ma+μkMg
and block m:
Tb=F-μkmg-ma

so I said since larger mass has larger KInetic Friction Fk, compared to the small one, and because of comparing the Ta equation of M and the Tb equation of M then Tb I guess is bigger.
I don't know if I
am right or not.

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berkeman
Several things. First, the problem doesn’t explicitly state it, but you should evaluate this at constant velocity, ie a=0. Second, your approach is more complicated than it needs to be. You wind up with answers in “F” which you don’t know. You can figure out F but why bother? Look at figure a). What is the tension if m is 0? Clearly the tension is all about block m, and you can evaluate it considering only the forces on m. Similarly in case b you need only evaluate the forces on M.

SakuRERE
Cutter Ketch said:
Several things. First, the problem doesn’t explicitly state it, but you should evaluate this at constant velocity, ie a=0. Second, your approach is more complicated than it needs to be. You wind up with answers in “F” which you don’t know. You can figure out F but why bother? Look at figure a). What is the tension if m is 0? Clearly the tension is all about block m, and you can evaluate it considering only the forces on m. Similarly in case b you need only evaluate the forces on M.

I Knew i was complicating things more than how it should be.
So just to make sure, It's all about that mass being dragged by the rope, and since at the second situation The bigger mass and one having bigger fk then considering the system having the same acceleration :
Tb of M= Ma+fk
Ta of m= ma+fk
so Tb>Ta
thanks again

SakuRERE said:
Tb of M= Ma+fk
Ta of m= ma+fk
so Tb>Ta

Like I said,I would take a to be 0, so in what you wrote above it wouldn’t be clear which is larger. However you wrote “fk” in both, which I presume means the force from sliding friction. Is that the same in the two cases? What is the magnitude of the frictional force in terms of the mass?

SakuRERE
Cutter Ketch said:
Like I said,I would take a to be 0, so in what you wrote above it wouldn’t be clear which is larger. However you wrote “fk” in both, which I presume means the force from sliding friction. Is that the same in the two cases? What is the magnitude of the frictional force in terms of the mass?
you're right, I must have written Fk of M and Fk of m,
since Fk= μk*Fn (Fn is the normal force) and it's mentioned that both blocks have the same μk
so we know both blocks have different masses and then they have different Fn because of Fn=Fg=mg (weight)
and I think there is no problem considering the acceleration a= constant value rather than a=zero since all other variables we know how they are different in each block.

SakuRERE said:
you're right, I must have written Fk of M and Fk of m,
since Fk= μk*Fn (Fn is the normal force) and it's mentioned that both blocks have the same μk
so we know both blocks have different masses and then they have different Fn because of Fn=Fg=mg (weight)
and I think there is no problem considering the acceleration a= constant value rather than a=zero since all other variables we know how they are different in each block.

True. Your answer is more general and you see both terms are proportional to mass. However I wanted you to show that the second term is proportional to mass as I believe that is the point of the question (the first term having nothing to do with friction)

SakuRERE
Cutter Ketch said:
True. Your answer is more general and you see both terms are proportional to mass. However I wanted you to show that the second term is proportional to mass as I believe that is the point of the question (the first term having nothing to do with friction)
I do get what you mean, I have always been afraid of coming with assumptions from my mind. But at the end, you are an expert, and I see why you suggest studying the system when a=0 because we already have the mass (which is the only important thing in the first term) in the second term as a weight. I wish I got your idea right.
thanks again

## 1. What is friction?

Friction is a force that resists the relative motion between two surfaces in contact with each other. It occurs due to the microscopic irregularities on the surfaces that interact with each other.

## 2. How does mass affect friction?

The greater the mass of an object, the greater the force of friction it experiences. This is because the weight of the object increases with its mass, which in turn increases the normal force between the surfaces in contact, leading to a higher amount of friction.

## 3. What is the difference between static and kinetic friction?

Static friction is the force that resists the movement of an object when it is at rest, while kinetic friction is the force that opposes the motion of an object when it is in motion.

## 4. How does tension affect friction?

Tension, or the pulling force applied to an object, can either increase or decrease the force of friction depending on the direction and magnitude of the tension force. If the tension force is parallel to the surface, it can reduce the friction force, while if it is perpendicular, it can increase the friction force.

## 5. What factors can affect the amount of friction between two surfaces?

The amount of friction between two surfaces is affected by the type of surfaces, the weight or mass of the objects, the roughness of the surfaces, and the presence of any lubricants or contaminants on the surfaces.

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