# Friction problem -- 2 Blocks Sliding on a Surface

## Homework Statement

A block of mass m=2kg and one of mass M=8kg have initial velocity zero.
The friction coeffecient between m and M blocks is 0.3
Between block M and the surfasse there is no friction.
L=3 metres
F is a force constant and horizontal with magnitude 10 N, applied on block m and so block m starts to move and goes to left extremity of block M.
block M also moved as you can see in the image

1) How long does it takes to block m to arrive to left extremity of block M?

2? What is the value of the displacement of block M?

the image is:

## The Attempt at a Solution

[/B]
i put the forces applied in each block:
block 1:
x: ma1=F-F(of friction)
y: mg=Normal force 1

block 2:
x: Ma2=F(of friction)
y: Mg=Normal force 2

and then i took a2 (acceleration of block 2) = 0.735 m s^-2

i tried to use v^2=v^2 (initial) +2ax
but i dont know v neither x....any suggestion?

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PeroK
Homework Helper
Gold Member
2020 Award

## Homework Statement

A block of mass m=2kg and one of mass M=8kg have initial velocity zero.
The friction coeffecient between m and M blocks is 0.3
Between block M and the surfasse there is no friction.
L=3 metres
F is a force constant and horizontal with magnitude 10 N, applied on block m and so block m starts to move and goes to left extremity of block M.
block M also moved as you can see in the image

1) How long does it takes to block m to arrive to left extremity of block M?

2? What is the value of the displacement of block M?

the image is:

## The Attempt at a Solution

[/B]
i put the forces applied in each block:
block 1:
x: ma1=F-F(of friction)
y: mg=Normal force 1

block 2:
x: Ma2=F(of friction)
y: Mg=Normal force 2

and then i took a2 (acceleration of block 2) = 0.735 m s^-2

i tried to use v^2=v^2 (initial) +2ax
but i dont know v neither x....any suggestion?

What about looking first at the relative motion of block m with respect to block M?

Although you have an image, I suggest you to draw a free body diagram representing all the forces that are involved in the situation (in the image just appears one). Then see what happens. Is there constant velocity?

For there to be motion of something, there must be a force acting on that something.

Doc Al
Mentor
and then i took a2 (acceleration of block 2) = 0.735 m s^-2
Good. What's the acceleration of block 1?

i tried to use v^2=v^2 (initial) +2ax
but i dont know v neither x....any suggestion?
Well, you do know the distance... the relative distance. Since you don't know v, you might want to choose another kinematic formula.

Good. What's the acceleration of block 1?

Well, you do know the distance... the relative distance. Since you don't know v, you might want to choose another kinematic formula.

I cant calculate acceleration of block 1 because it is in an accelerated frame and so the second law of Newton is not valid

I tried to use Energy-Work Theorem but i cant because i dont have enough information to use it

PeroK
Homework Helper
Gold Member
2020 Award
I cant calculate acceleration of block 1 because it is in an accelerated frame and so the second law of Newton is not valid

I tried to use Energy-Work Theorem but i cant because i dont have enough information to use it

Suppose two racing cars started at the same time. One accelerated at ##a \ ms^{-2}## and one accelrated at ##b \ ms^{-2}## and you measured the distance between them over time.

Suppose you repeated this and the first car failed to start and the second car accelerated at ##(b-a) \ ms^{-2}## and you measured the distance between them over time.

Would there be any difference?

Doc Al
Mentor
I cant calculate acceleration of block 1 because it is in an accelerated frame and so the second law of Newton is not valid
You can calculate the acceleration of block 1 exactly as you calculated the acceleration of block 2: By applying Newton's 2nd law from the inertial frame of the ground. Those accelerations will be with respect to the ground. It's up to you to figure out the relative acceleration of block 1 with respect to block 2.

I tried to use Energy-Work Theorem but i cant because i dont have enough information to use it
You won't need the work-energy theorem; stick to Newton's 2nd law and kinematics.