mit 2 FRQ Possible Questions
M
Note: Figure not drawn to scale.
A long track, inclined at an angle 0 to the horizontal, has small speed bumps on it. The bumps are evenly spaced a
distance d apart, as shown in the figure above. The track is actually much longer than shown, with over 100
bumps. A cart of mass M is released from rest at the top of the track. A student notices that after reaching the 40th
bump the cart's average speed between successive bumps no longer increases, reaching a maximum value Vavg
This means the time interval taken to move from one bump to the next bump becomes constant.
a. Consider the cart's motion between bump 41 and bump 44.
i. In the figure below, sketch a graph of the cart's velocity v as a function of time from the
moment it reaches bump 41 until the moment it reaches bump 44.
=
ii. Over the same time interval, draw a dashed horizontal line at v Vavg. Label the line "Vavg"
-Time
Bump Bump Bump Bump
41
42
43
44
b. Suppose the distance between the bumps is increased but everything else stays the same. Is the maximum
speed of the cart now greater than, less than, or the same as it was with the bumps closer together?
Greater than
Less than
The same as
By increasing the distance between
bumps, you also increase the time
it
to reach that distance, giving the cart Some accel
Briefly explain your reasoning. before becoming a higher constant velocity.
c. With the bumps returned to the original spacing, the track is tilted to a greater ramp angle 0. Is the
maximum speed of the cart greater than, less than, or the same as it was when the ramp angle was
smaller?
