A wheel with a radius of 3 cm is being pushed up a ramp at a rate of 7 cm per second. The ramp is 640 cm long, and 200 cm tall at the end. A point P is marked on the circle as shown (picture is not to scale).

Question

wheelonramp.gif

1. Traveling at 7 cm/sec, how long does it take the wheel to complete one rotation?

2. What is the initial height of the center of wheel?

3. Traveling at 7 cm/sec, in one second, how much does the height of the center of wheel increase?

4. Write an equation for the height of the center of the wheel as a function of t, time in seconds.

5. Write an equation for the height of the point P above the ground as a function of t, time in seconds.

Answer 1

#1. C = 6π cm, so it takes 6π/7 = 2.69 seconds to rotate once
#2. No idea where P is, but the plane is inclined at an angle of
Ø = arctan(200/640) = 17.35°
So, if P is such that the radius from the center of the wheel is perpendicular to the ramp, and the bottom of the ramp is at (0,0), then P = (-3sinØ,3cosØ)
#3. the center travels vertically at 7sinØ cm/s
#4. should be obvious
#5. see what you can do here. Without knowing where P started, I don't want to bother doing the calculation. But you know that the angle θ grows by w=2πf = 2π * 7/(6π) = 7/3 rad/s