- #1
Nicholas Egebak
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Homework Statement
A small box (mass m1) is placed upon a large box (mass m2); the large box i placed on a horizontal table. The boxes begin a rest on the table. The lower box is hit by a horizontal blow at the time t=0 resulting in a initial velocity v0. The frictioncoefficient between all surfaces are µk
Homework Equations
a) Draw force-diagrams for both boxes as the move relative to each other. Indicate all Newtons-Third-Law-Pairs.
b) Determine all velocities and accelerations of the boxes as the move relative to each other. At what time T do the boxes not move relative to each other anymore?
c) Determine the acceleration of the boxes when they do not move relative to each other. What length L do the boxes move in this fase? The initial velocity can be concidered know as v1
The Attempt at a Solution
I started drawing the force diagrams. No problem there. It was easy to see that the normal force in both cases were pairing up with the gravitational force.
For question b) I came up with this equation:
vbox1=v0-a*t
Applied on the second box (the one underneath the other):The acceleration must be the kinetic friction force divided by the mass:
vbox1=v0-(fk)/m*t
Naturally I got:vbox1=v0-μk*g*t
For the box on top:
vbox2=-μk*g*t
For the acceleration I differentiate both:
abox1=(vbox2)'=-g*µk
abox2=(vbox2)'=-g*µk
It is now that I am lost. I do not know how to find the time by which the boxes are not moving relatively to each other anymore...
Picture of scenario:
Force Diagrams: