# Box friction kinematics (1 Viewer)

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#### unscientific

Guys...im just a high school student and im presented with a ' challenge ' by my physics teacher. I really hope to solve this by myself...but i hope you guys can give me tips on solving this problem..thnx

Imagine a big box on a surface with friction = 0 and a smaller object is thrown on top of with with a force denoted F. Can we calculate when will the smaller object move in phase with the bigger object? with regard with the distance travelled by the big box. ( in the sense that the smaller object stops moving??)

Thnx alot. I mean that if there is a given velocity and everything is given, is there a way to find out how much distance the big box has moved when the small object on it stopped moving?

Is there any other simpler ways to solve it in terms of kinematics?

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#### Farsight

If friction is zero the big box won't ever stop moving. And there's no mention of relative masses or velocities, so maybe it's a trick question.

#### Hootenanny

Staff Emeritus
Gold Member
unscientific said:
I mean that if there is a given velocity and everything is given, is there a way to find out how much distance the big box has moved when the small object on it stopped moving?
If the co-efficient of friction between the big box and little box is known (in addition to the masses and initial velocities etc.), then yes it is possible.

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#### Astronuc

Staff Emeritus
Can we calculate when will the smaller object move in phase with the bigger object?
Is the small object (box) oscillating?

The boxes will move 'together' if the friction is sufficient to allow the big box to catch the smaller box. One has to look at the static and dynamic coefficients of friction.

The smaller box has to decelerate while the larger box has to accelerate - to the same velocity. One must develop the equation(s) for that.

In phase means the same velocity as a function of time, so force (F), static coefficient of friction and relative masses play a role.

im not sure i got this right...
the small box moves on top of the big box, and friction is applied.
the big box is at rest, and the small one has a starting velocity ?

if so, its easy to determin it by energy speculations...
we know that the friction causes a loss of velocity to the small box, and that energy must be trassfered to the big object (if we ignore heat and noise...).
so if we can determin the energy of the big box in the end of the process, when the small object stops moving on the big box, then we can determain the work made by the friction.

big box: mass- M V0b=0 Vb=the speed in the end of the process.
small box: mass:m v0s>0 Vs=the speed in the end of the process.

so the energy is being conserved by the equation:
0.5mV0s^2= 0.5mVs^2 + 0.5MVb^2
but we know that in the end of the process the small box stops moving on the big box, so in the end, Vs=Vb=V, therefor:
0.5mV0^2=0.5mV^2+0.5MV^2
V=sqrt(m/(M+m)) * V0s

so Eb=0.5MV^2
and we know that
Wfriction=fX=Eb
X=Eb/f

then:
X=0.5MV^2=(0.5mMV0s^2/f(M+m))

im very tierd so i might be wrong...

Astronuc said:
Is the small object (box) oscillating?

The boxes will move 'together' if the friction is sufficient to allow the big box to catch the smaller box. One has to look at the static and dynamic coefficients of friction.

The smaller box has to decelerate while the larger box has to accelerate - to the same velocity. One must develop the equation(s) for that.

In phase means the same velocity as a function of time, so force (F), static coefficient of friction and relative masses play a role.
energy method was developed to avoid such complication, though it much more cool and intuitive, its mindbreaking sometimes...

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