# Find the Contact Force Between Two Blocks

• am08
In summary: Since M1 is pushing on M2, the force acting on M1 must be greater than the force acting on M2. Therefore, the force that is acting on M1 is 4.55 N - 1.51 N = 3.3 N.
am08
Two blocks are in contact on a frictionless table. A horizontal force F is applied to M2, as shown. If M1 = 1.51kg, M2 = 3.96kg, and F = 4.55N, find the size of the contact force between the two blocks.

So first I found the acceleration (F=ma)

4.55/(1.51+3.96) = 0.83 = acceleration

Im suck from here

Try drawing a free-body diagram of M1, to make this easier. What forces are acting on it? You also know its acceleration, so what forces are causing this acceleration?

the horizontal force that was applied to M2...

If the force on M2 was also applied to M1 like you said, M1's acceleration would not be the 0.83 m/s^2 you calculated. So, a different force must be causing this acceleration...

would gravity play a factor?

Last edited:
No, let me explain this differently. Now, draw the free body diagram of M2. There's the 4.55 N force acting on it, but there is another horizontal force acting in the opposite direction, the contact force. Newton's Third Law states there are equal and opposite forces, so this applies to the contact force. So, the contact force is acting on M1, giving it its acceleration, if I'm thinking of this problem right (force acting on M2, and M2 is pushing on M1). Does this help? I deeply apologize if I overcomplicated the problem.

Last edited:
So the contact force is the force acting in the opposite direction?

Which would be .83*1.51 =1.25 N is that the contact force?

or do I do 4.55 N - 1.51 N = 3.3 N

and you that's the problem.. m2 is pushing m1

The contact force is merely the mass of M1 times its acceleration. Remember, the contact force is the force giving M1 its acceleration. Do you see why?

im sorry terbum, this is just so confusing for me.. probably b/c it's getting late..

so how do i find the acceleration of M1 if it isn't 0.83m/s^2

The acceleration you solved for was the acceleration for the system. So, BOTH M1 and M2 have an acceleration of 0.83 m/s^2.

Yeah, I had a tough time with this topic when I learned it, too. It does get a little confusing. I guess if you want to learn it, keep doing problems. Practice never hurts.

am08 said:
so how do i find the acceleration of M1 if it isn't 0.83m/s^2

The accn of M1 is 0.83 m/s^2, as you have calculated. A force of 4.55 N is pushing on M2, which in turn is pushing on M1, and both masses are moving together, and so their accn must be same.

The last step remaining is to find out what force acting on M1 produces an accn of 0.83 m/s^2? You know mass of M1, and accn 'a'. Apply Newton's 2nd law.

## 1. What is the contact force between two blocks?

The contact force between two blocks is the force that exists between the two blocks when they are in direct contact with each other. It is a result of the interaction between the molecules of the two surfaces and is responsible for keeping the blocks together.

## 2. How is the contact force calculated?

The contact force is calculated using Newton's third law of motion, which states that for every action, there is an equal and opposite reaction. This means that the contact force between two blocks is equal in magnitude and opposite in direction.

## 3. What factors affect the contact force between two blocks?

The contact force between two blocks can be affected by the mass of the blocks, the surface area in contact, and the coefficient of friction between the two surfaces. These factors determine the magnitude of the contact force.

## 4. Can the contact force between two blocks be greater than the weight of the blocks?

Yes, the contact force between two blocks can be greater than the weight of the blocks. This is because the weight of the blocks is only one of the factors that determine the magnitude of the contact force. Other factors, such as the coefficient of friction and the surface area in contact, can also contribute to a greater contact force.

## 5. How does the contact force between two blocks affect their motion?

The contact force between two blocks can either cause them to move together or prevent them from moving. If the contact force is greater than the force of gravity, the blocks will move together. However, if the contact force is less than the force of gravity, the blocks will remain stationary.

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