Motion on a Rough Inclined Plane

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Motion on a Rough Inclined Plane
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A trolley of mass 0.5 kg is released from rest
at a point O on a rough runway inclined at 30o
to the horizontal. It slides down the runway and
the velocity-time graph is given below. Assume
g 10 m s-2
Determine the friction and normal reaction on the
trolley.
3
A trolley of mass 0.5 kg is released from rest
at a point O on a rough runway inclined at 30o
to the horizontal. It slides down the runway and
the velocity-time graph is given below. Assume
g 10 m s-2
From the velocity-time graph the acceleration of
the trolley is 4 m s-2. The acceleration vector
points down-slope.
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In the direction perpendicular to the inclined
plane, there is NO motion.
Normal Reaction R mg cos q 0.5 10 cos
30o 4.33 N
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In the direction along the inclined plane, there
is MOTION.
Apply F ma mg sin q - Q ma Q mg sin q -
ma Q 0.5 10 sin 30o - 0.5 4 2.5 -
2.0 0.5 N
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At a certain inclination of the runway, the
trolley can move down-slope with uniform velocity
after given a push. Find the value q for this to
occur.
Q 0.5 N
The forces along the inclined should be
balanced mg sin q Q 0.5 10 sin q 0.5 q
5.74o
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At q 5.74o , the runway is friction-compensated.
Q 0.5 N mg sin 5.74o 0.5 N
At this inclination, the friction is balanced by
the down-slope component of the weight.
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In doing experiments concerning a trolley moving
on a horizontal runway, friction affects the
results of the experiment.
By sloping the runway at a certain angle (usually
very small) with the horizontal, the effect of
friction can be canceled. The runway is said to
be friction-compensated.
To find the inclination of the runway for
friction compensation, the runway can be slightly
inclined and then a trolley on it is given a
push. If the trolley moves down the runway with
uniform velocity, it is friction-compensated.
Otherwise the inclination is adjusted again. The
velocity of the trolley can be studied using a
ticker-tape timer or a motion sensor.