The Physics Philes, lesson 66: Walk the Plank!
As promised last week, I’m back with a sample problem dealing with a body’s center of gravity! So let’s dive right in, shall we?
Let’s say you have a wooden plank that is 6.0 m long and weighs 90 kg. You set the plank of wood on top of two sawhorses that are 1.3 m apart. The sawhorses are located the same distance away from the center of the plank. You decide it would be a good idea to try to stand on the right-hand end of the plank. Because YOLO, I guess. If the plank is to remain at rest, how massive can you be?
Let’s draw this out first.
Admit it. You were wondering what sawhorses were. Now you know. What else do we know from this drawing? We know the length L of the plank, the distance D between the sawhorses, the mass of the plank, the location of the center of the plank and the system’s center of gravity, and the distance between the right sawhorse and the right end of the plank. What we don’t know is how massive you can be in order for the plank to remain at rest. That is are target variable.
If we consider the geometric center and the center of gravity of a uniform plank to be the origin, the positive x-axis points to the right. That makes the x-coordinates of the centers of gravity x_p = 0 and the x-coordinate of you is x_t = L/2 = 3.0 m. Now we can find the center of gravity of the system. We’ll us the following equation to figure this out:
(Usually we’d need to figure out the centers of gravity for the y- and z-axes, but we’re only dealing with the x-axis here.)
When we plug in the numbers, we get:
If we set this equal to D/2 – which is the x-coordinate of the right-hand sawhorse, we get:
Ta-da! In order to keep the wooden plank in balance, you cannot weigh any more than 30 kg.
That’s all for today. But next week I’ll be back talking about stress and strain.
Featured image credit: Horia Varlan