At the State Fair you see people trying to win a prize at a game booth. They are sliding a metal disk shaped like a puck up a wooden ramp so that it stops in a marked zone near the top of the ramp before sliding back down. You estimate that you can slide the 'puck' at 8.0 ft/sec, but would that win the game? The two boundaries of the zone appear to be at 10 and 10.5 feet from the bottom of the ramp where you release the 'puck.' The ramp appears to be inclined at 37° from the horizontal. You happen to remember that between steel and wood, the coefficients of static and kinetic friction are 0.1 and 0.08, respectively. The weight of the 'puck' is about 2.5 lbs.
(a) What is the algebraic expression for the distance up the ramp you slide the puck in terms of the initial speed with which you slide the puck (V), the angle of the ramp (θ), the coefficients of static and kinetic friction (
μS
and
μK
), the weight of the puck (W), and the gravitational acceleration (g)? [Note: Don't enter an equation like "x=blah". Just enter the "blah" part. All letters are capital except for "g".]
(b) What is the numerical value of the distance you slide the puck up the ramp (make sure to include units and put a space between the number and the units or else the system will not recognize it!!)?