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Class Notes Physics I, 9/14/98
Work and Acceleration on a Ramp
Experiment: We determine whether the produce Fnet `ds for a cart rolling down
a ramp is linearly related to velocity change or to the change in squared velocity.
If a cart coasts down an incline at constant velocity, when 'held back' by a
force equal to the weight of a number of washers, then when the cart coasts down that
incline in the absence of the washers, it will be accelerated by a net force equal to the
weight of the washers.
- We can determine the velocity attained by the cart by timing it as it accelerates
from rest through a known distance.
- The equations of motion tell us that the result of the acceleration through the
known distance is to increase v^2 by 2 a `ds, or alternatively to increase 1/2 v^2 by a
`ds. A graph of change in 1/2 v^2 vs. a `ds should therefore be a straight line with
slope 1.
- Since the net force on the cart is directly proportional to its acceleration a, a
graph of the change in v^2 vs. Fnet `ds should also give a straight line.
We pose the following questions:
- Explain why a `ds is equal to the change in 1/2 v^2.
- Explain why the change in v, per unit of slope, is less and less as the slope
increases.
- Explain in detail why we expect Fnet `ds to be proportional to the change in v^2.
- Explain why it is not important whether we measure force in units of (uniform)
washer-weights, Newtons, pounds or tons.
http://youtu.be/e581uzIR1ag
http://youtu.be/gOKCaV-Tw10
http://youtu.be/jrUQMlcUiDA
Using a pulley-and-ramp system, we can determine for different numbers of washers the
ramp slopes for which the washers, when suspended over the pulley by a thread attached to
a toy car or truck, will permit the vehicle to move at a constant speed down the ramp.
- For each number of washers we call this slope the constant-velocity slope.
For each slope we then allow the vehicle to coast down the ramp for a known distance,
starting from rest.
- We wish to determine the final velocity attained in each case, assuming a constant
acceleration.
- In order to determine the final velocity we time the cart through known distance.
- The data we obtain will be something like that shown below, but with more data points.
We then graph final velocity versus the product F `ds, where F is the number of
washers.
- We interpret F as the force
exerted by gravity on the washers, measured in units of 'washers'.
- We obtain a graph something like
that shown below, where we attempt to determine whether the graph is linear or not.
- We then graph vf^2 vs. F `ds and
determine whether this graph is linear.
http://youtu.be/5cNRxKNgGKE
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