Page 106 - Making things move_ DIY mechanisms for inventors, hobbyists, and artists

Chapter 4 Forces, Friction, and Torque (Oh My!) 87

FIGURE 4-11 Free body diagram of paint can platform in Graffbot (left) and rope forces
broken up into components (right)

opposite, and therefore cancel each other out, satisfying our first condition for static
equilibrium. That leaves us with just two up forces (F and F ) and one down force
1-UP 2-UP
(W). In order for the system to balance, the up forces need to equal the down forces
to satisfy the second condition for static equilibrium:

F + F = Weight
1-UP 2-UP
So if the paint can platform weighs 10 lbs, each F force must be 5 lbs. There are no
UP
torques on this paint platform, so we can ignore the third condition for static
equilibrium.

Now we’re getting closer. We know the F OUT forces cancel, and each F force is 5 lbs.
UP
But we don’t know the actual forces, F and F , on the ropes that go to the spools. For
1 2
the triangle on the right in Figure 4-11, recall from our earlier conversation that the
sine of an angle equals the opposite side over the hypotenuse (the SOH part of
SOHCAHTOA):

sin 45° = F / F
1-UP 1
This gives us F = 7 lbs. So we learned that it takes more force to pull something up at
1
an angle like this than it takes to pull something up straight. If the angle gets smaller,
so that the paint can platform starts closer to the motor spools, the force on the ropes
will increase.