Description : A Bee is placed on a friction-less
inclined plane (hey, work with me here, you know how hard it is to draw a
box at an angle?). It can be given an velocity (upward or downward). The
angle of the incline can be changed. The mass of the Bee can be changed.
You can also add a force applied up the incline (such as a tension in a
string attached to the Bee, or a force pushing the Bee). The angle for the
force is measured from the "true horizontal" (thus, if you want
the force to be directed up the incline .. give it the same angle as the
incline). [The one thing I left fixed was the starting position of the Bee
.. changing that is not as important as changing the other things {in case
you are wondering, the Bee start 6 meters up, as measured along the
incline}.] [Also note: this Bee is on a "track" on the incline
.. thus you can't "lift" him/her off the incline with the
applied force - a future version of this page might allow that.]
net Force (upward_along_incline) = Fx - mgsin(theta) = ma
[Note, the direction up the incline = positive for the
velocity and the acceleration!]
Try these investigations :
a) Can you find a force, for a given situation {with no initial
velocity}, where the Bee won't move on the incline? Can you also calculate
that force?
b) Consider the situation above - with that specific force .. what if
you now put in an initial velocity ... what is the acceleration of the
system? Does that make sense? Why?
c) If the Force is zero ... the amount of mass of the bee does not
affect the acceleration, right? Why not?
d) With F=0, give the Bee an initial velocity up the incline, then
same magnitude down .. watch the velocity at the bottom - do both cases
have the same final velocity? Is that what you expect?
e) With no initial velocity, and the force initially zero, watch the
final velocity when it reaches the bottom. Then apply a small force upward
along the incline, and watch the final velocity - how has it changed?
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