This Too Shall Pass: The Physics Behind OK GO's Music Video Stunt?

[yuntsewu]

This Too Shall Pass<-- need help!

Homework Statement

In the video for the song “This Too Shall Pass,” the band OK GO hired a team of physicists and engineers (seriously!) to build a giant machine with parts that moved in sync with the music. Part of the video shows a tire rolling down an inclined track, then along a straight section of track, and finally hitting a hammer (which turns on a fan, which blows an umbrella, etc…). According to the band’s website:
The tire ramp had to be lubricated with white lithium grease between each take to ensure the correct amount of friction for the timing. Too little and the tire would slow down and grind almost to a halt. Too much, and it would rocket down the ramp and smash the mallet so hard it would pop out of the rails.
The tire takes about 3 seconds to roll down the inclined section of the track. The incline is at 7.5° from horizontal. The tire rolls along the flat part for about 2 seconds.
1. Estimate the kinetic energy of the tire (mass is approximately 25 lbs) when it reaches the bottom of the inclined portion of the ramp.

Homework Equations

Emec=dK+dU=0
Ke=1/2mv^2
U=mgh

The Attempt at a Solution

I tried using Fnet but no good, can't find force friction going down the slope. if i neglect force friction, i get a really small number for acceleratoin; which is not possible.

 

[jbsteele]

The correct solution is to use the work-energy principle. The total change in energy of the tire is zero since it starts and ends at the same height (the track is level). Therefore, the change in kinetic energy is equal to the change in gravitational potential energy:dK + dU = 0dK = -dUdK = -mghK = 1/2 mv^2 = -mghv^2 = 2ghv = sqrt(2gh)For a 25 lb tire on a 7.5° incline, K = (25 lb)(32.2 ft/s^2)(2)(7.5 ft) = 2450 ft-lb