Pulling a Carpet: Min Force & Velocity of Centre of Mass

[Titan97]

Homework Statement

A long pliable carpet is laid on the floor. One end of the carpet is bent back and then pulled backwards with constant velocity $v$. Find the velocity of centre of mass of the moving part and the minimum force required to pull the moving part.

Homework Equations

$P=mv$

The Attempt at a Solution

If the end of the carpet that is pulled backwards, moves a distance $2x$, then the bent part will move a distance $x$ and after some calculations, I found that the midpoint shifted by a distance $\frac{3x}{2}$.

• If each part of the carpet is moving with different velocities, then won't the carpet stretch?
• Also, for finding force, $$F=\frac{dM}{dt}v$$ Which $v$ should I use?
• Finally, some points in the carpet will experience a jerk and suddenly acquire a velocity. So I can't use conservation of energy right?

 

[Simon Bridge]

The different parts of the carpet are not moving with different velocities - the centre of mass is a geometric location, not physically part of the carpet. The part of the carpet that corresponds to "the middle" keeps changing.

Newton's Law is for the force acting through the centre of mass.

You are adding energy to the carpet via whatever pulls on the carpet.

 

[drvrm]

to calculate the force required you better use change in momentum

 

[Titan97]

@Simon Bridge it's given in the solution to "observe that it's not P=mv_cm"

 

[Simon Bridge]

See dvrm reply post #3

 

[Titan97]

That's is what I did. What is v?

 

[drvrm]

Find the velocity of centre of mass of the moving part and the minimum force required to pull the moving part.

to calculate the force required you better use change in momentum

the required force must be equal to rate of change of momentum -
write down the the equation and see whether you can calculate the force and velocity-
take a portion of the carpet moved by the action of force...
how you can calculate v - by energy considerations or impulse...