Frictionless
Motion Up and Down an Incline
In the absence of friction, the only force
acting on the cart in the direction of travel (x-direction) is a component
of the gravitational force, F=mgsinØ, which points in the positive
x-direction independent of the cart's direction of travel. Consequently,
in the absence of friction, the acceleration maintains a constant value,
a=gsinØ, as the cart moves up and down the incline
(Lecture 7).
Effect of Friction on Motion Up and Down an Incline
While the gravitational force on the cart always points
in the same direction, independent of the cart's motion, the frictional
force (Fk) acts in a direction opposite that of the cart's
motion. Consequently, in the presence of friction, the net force acting
on the cart as it moves up the incline, F = mgsinØ + Fk,
is larger than the net force acting on the cart as it moves down the
incline, F = mgsinØ - Fk. The corresponding acceleration
of the cart while moving up the incline, aup = gsinØ +
Fk/m, is larger than the acceleration of the cart while moving
down the incline, adown = gsinØ - Fk/m. The
magnitude of the frictional force, Fk, can be determined from
the difference between the "up" and "down" accelerations, aup
- adown = 2Fk/m, where m is the mass of the cart
(Lecture 7).
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