Day 73: Desmos, Direct Measurement Videos, and a Classic Physics Problem
AP Physics C: This is a classic problem (which also was on the 1983 AP Physics C Mechanics exam). At what angle will the block lose contact with the wheel?
We cranked through the physics and got around 48 degrees. Then I showed the class the video, but it looks like it’s still in contact with the wheel at 48 degrees (screenshot below).
So we decided to take another approach for verification: If the block really leaves the wheel at 48 degrees, how far from the center of the wheel will the block be as it passes through the horizontal? The video shows around 35 cm. (screenshot below).
So again we crunched through some physics. But instead of solving a series of simultaneous equations for projectile motion, we modeled those equations in Desmos instead.
The red graph represents the vertical position of the block over time. The green graph is the time at which the block reaches the horizontal (about 0.12 second). The blue graph represents the horizontal position of the block over time. So the intersection of the blue and green graphs will tell us the horizontal position of the block as it passes through the horizontal. And look — 35 cm! So even though it’s tough to tell that the block looses contact with the wheel at 48 degrees, the resulting projectile motion holds up.