# What Is the Upward Acceleration of m2 in a Friction-Influenced Pulley System?

In summary: I can't really help you there.The coefficient of kinetic friction between m1 and the sur-face is 0.201.The force acting on m1 is Fg=265.58 going down and Fy=126.338 going up because of the angle it is pulled at. So then I figured Fn would be 265.58-126.338=139.242. And Fx=190.876. And the Fk=.201(139.242)=27.9876. Then m2 would have an Fg=55.86. The upwards acceleration of m2 is Fx-Fk-Fgm2=107.028. Then I

## Homework Statement

A 27.1-kg block (m1) is on a horizontal surface,
connected to a 5.7-kg block (m2) by a massless string as
shown in the Figure. The pulley is massless and friction-
less. A force of 228.9 N acts on m1 at an angle of 33.5◦.
The coefficient of kinetic friction between m1 and the sur-
face is 0.201. Determine the upward acceleration of m2.

(m2 is dangling off the ledge by the pully connected to m1)

Fg=mg
F=ma
Fk=uk(Fn)

## The Attempt at a Solution

I drew all the forces, m1 would have Fg=265.58 going down and Fy=126.338 going up because of the angle it is pulled at. So then I figured Fn would be 265.58-126.338=139.242. And Fx=190.876. And the Fk=.201(139.242)=27.9876. Then m2 would have an Fg=55.86.

I found net force= Fx-Fk-Fgm2=107.028. Then I used F=ma to try and find upward accel of m2. I figured since the force is being applied to m1 and it is connected to m2 I would use the combined mass of both of them and do 107.028=(5.7+27.1)(a) and a came out to be 3.26305m/s^2 but it turns out that was wrong. Can anybody help me find the real answer?

What forces act on m1 and m2? You have Fg for both blocks, Fn and Fk for m1, but what else?

Think of what connects the blocks; there's a force you are forgetting. (Hint: since the pulley is massless and frictionless, the upward acceleration of m2 is the same as the rightward acceleration of m1.)

Well for me the block is being pushed to the left, friction to the right. But I am assuming you meant the upwards acceleration for m1 would be the same as the leftward(for me) acceleration for m1. I knew that already. But I have no idea what force I am missing.

If the block were being pushed to the left, the hanging block m2 would have a downwards acceleration. From your description, the system sounds like this to me:

Regarding the missing force, are you familiar with tension?

Yea that image looks right, mine was just flipped the other way around but that's fine too. But no I am not sure how to find tension in this problem. Thank you for helping me btw.

Tension pulls on each end of the rope. When we look at each body in isolation, we "cut" the rope, so there is a tension force acting on each block. By Newton's 3rd law, the forces are equal and opposite, so the tensions on block 1 and block 2 are the same. (This is a bit simplistic of an explanation, and is only true if the pulley is massless and frictionless.)

So, there is a tensile force to the left on block 1 and an upwards tensile force on block 2.

You can solve for tension in block 2 and substitute that into your forces on x for block 1 and then solve for a.

Okay well I tried doing something... I'm not sure if its right.

assuming my force F is 107.028 then,

T-F=m1a

so T=m1a+F

and m2g-T=m2a

so replacing T as (m1a+F) i get... m2g-(m1a+F)=m2a

that comes out to be a=(m2g-F)/(m1+m2)

so I plugged in the numbers a=(55.86-107.028)/(27.1+5.7)=-1.56m/s^2 is that right?

>>T-F=m1a

where is your friction, and F has two components ... you need to break them up.

It would look something like this in the X

Forces in X = Fpcos(t) - T- Ff = (m1)a;

you can find friction by finding the normal force (sum the forces in the Y).

## 1. What is friction?

Friction is the resistance force that occurs when two objects are in contact and moving relative to each other.

## 2. How is friction measured?

Friction is typically measured using a device called a friction force sensor, which measures the force required to overcome the frictional force between two surfaces.

## 3. How does the angle of a force affect friction?

The angle of a force can affect the amount of friction between two objects. If the force is applied parallel to the surface, there will be more friction than if it is applied at an angle.

## 4. What is the relationship between friction and force at an angle?

The amount of friction between two surfaces at an angle is directly proportional to the perpendicular component of the applied force. The greater the perpendicular force, the greater the frictional force.

## 5. How can friction at an angle be reduced?

Friction at an angle can be reduced by using lubricants or by changing the angle of the applied force to be more parallel to the surface. Additionally, using smoother surfaces can also reduce friction at an angle.

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