Finding the distance traveled using Newton's laws and kinematics

[whoareyou]

Homework Statement

Homework Equations

Newtons' Laws
Kinematics Equations

The Attempt at a Solution

I don't know what I'm doing wrong, but I'm not getting the correct answer of 17cm ...

 

[ehild]

A will not stop. It comes to rest on the surface of B, that is they move together with the same velocity.

ehild

 

[whoareyou]

Does that imply that the time is wrong? Do I set up 2 equations, one for block A and block B and determine when their speeds will be the same?

 

[ehild]

Yes, the time is wrong. The force of friction decelerates A and accelerate B till their velocity becomes equal.

ehild

 

[whoareyou]

so...

3.5 - 5.88T = 4.704T
T = 0.331

d = (1/2)(4.704)(0.331)^2 = 0.257m --> still the wrong answer :(

 

[ehild]

You use wrong value for the acceleration of B. It should be the force of friction divided by 1 kg.

ehild

 

[whoareyou]

23.52N (the reaction force from the friction of block A) = ma

Now I assumed that it was the total mass of the system, since block A is on top of it and its moving with it. Was that assumption wrong?

23.52N = (m1 + m2)a
a = 23.52 / (m1+m2) = 23.52 / (4 +1 ) = 4.704m/s^2

 

[whoareyou]

Oh, okay I get the right answer now. But how come you don't use the total mass when finding the acceleration for B? It's directly on top of it ...

 

[ehild]

23.52N (the reaction force from the friction of block A) = ma

Now I assumed that it was the total mass of the system, since block A is on top of it and its moving with it. Was that assumption wrong?

23.52N = (m1 + m2)a
a = 23.52 / (m1+m2) = 23.52 / (4 +1 ) = 4.704m/s^2

It is wrong. Zero external force acts on the whole system. The blocks interact, the force of friction is an internal force. A acts B and B acts A through the friction. So block B moves according to the force exerted on it by block A: F= 23.52 N.

ehild

 

[whoareyou]

OH ! okay, makes sense. Thanks :)