Unformatted text preview: Homework 2 y’
x’ y m1
In class I did the problem of a block sliding on an inclined plane with friction.
When there was no friction I calculated the acceleration of the mass, which gave
a x ' = − g sin θ .
Notice that this acceleration is in the x’ direction, along the surface of the plane (not the
horizontal direction x). When I included friction and calculated the acceleration of the
sliding block I got.
a x ' = − g sin θ + μ k cos θ .
This makes sense because the extra term that appeared in the acceleration is positive and
tends to cancel the original term (which was negative). We expect this because friction
should reduce the acceleration. Also notice that if we let the friction coefficient go to
zero we recover the original equation.
Now, assume I add mass 2, which is attached to mass 1 by a string. Assume that
m2 is chosen so that the weight of m2 exactly cancels the dynamic friction force on the
sliding mass. Calculate the acceleration of the mass as a function of angle, the
acceleration of gravity and the friction coefficient (the masses should cancel out).
Before doing the calculation, ask yourself the following question. When you
include this additional mass in an attempt to cancel friction, is the acceleration with
friction and the friction-canceling weight less than, equal to, or larger than the
acceleration with no friction? (I asked this as a clicker question, but after discussions
after lecture is I think I did not make it clear which accelerations I was asking you to
compare. I wanted you to compare the acceleration when the mass m2 has been added to
the system to the acceleration of the mass with no friction, rather than to the frictionaffected acceleration.)
When you get the answer, show that it makes sense in the limit of vanishing
friction coefficient, and angle of 0º and 90º. ...
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