# What Are the Tensions in Two Blocks With Friction and Acceleration?

• Zywo
In summary, two blocks of mass 80 kg and 100 kg are attached by strings with a tension of 407 N and 137.2 N respectively. The system accelerates at 2 m/s^2 with a coefficient of friction of 0.14.
Zywo

## Homework Statement

Two blocks of mass m1=80 kg and m2=100 kg and attached by a string, another sting comes off of mass m1 and is pulled horizontally (kinda looks like this) (T1 & T2 are tensions)
m2--T2--m1--T1--> there is a coefficient of friction u=.14 for both blocks, what is the tension in both strings while the system accelerates at 2 m/s^2?

Fnet=ma
Ff=u(N)

## The Attempt at a Solution

Ok so for m1 horizontal forces are T1 to the right, T2 to the left and friction.
T2=(100)(9.8)(.14)=137.2 N Friction for m1=(80)(9.8)(.14)=109.8
So T1-T2-Ff = m1*a therefore T1=(80)(2)+(109.8)+137.2= 407 N
Is this Correct??
Thanks!

First consider the 2 block system as a 1 block system (combine their masses) then you can solve T1. Once you have this you can distribute T2 appropriately.

Your approach is correct, but there is a slight error in your calculation for T1. The correct value for T1 would be (80)(2) + 109.8 - 137.2 = 271.8 N. This is because the net force on m1 is equal to its mass times its acceleration, which is 80 kg * 2 m/s^2 = 160 N. Therefore, T1 must be equal to this net force minus the friction force and the force from m2 (which is T2). Keep up the good work!

## 1. What is friction?

Friction is a force that occurs when two surfaces come into contact and slide against each other, resisting the motion of one surface over the other.

## 2. How does friction affect pulling two blocks?

Friction plays a significant role in pulling two blocks. It opposes the motion of the blocks, making it harder to move them. The amount of friction depends on the nature of the surfaces in contact and the force applied.

## 3. What factors affect the friction between two blocks?

The amount of friction between two blocks is influenced by the roughness of the surfaces, the force applied, and the weight of the blocks. It also depends on the type of material the blocks are made of.

## 4. How can we reduce friction when pulling two blocks?

To reduce friction when pulling two blocks, you can use a lubricant like oil or grease on the surfaces in contact. You can also make the surfaces smoother by sanding or polishing them.

## 5. How do we calculate the friction force when pulling two blocks?

The friction force can be calculated using the formula F = μN, where F is the friction force, μ is the coefficient of friction, and N is the normal force exerted on the blocks. The coefficient of friction is a constant that depends on the materials in contact.

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