Quantitative FBDs

Quantitative FBDsJust like in units 1 & 2, our models (x-t, v-t, a-t graphs) didn’t really mean a whole lot if they couldn’t have predictive power• Because predictive power requires actual numbers (how fast something will be

going, how far something has traveled) we need to make sure our FBD models have predictive power as well

5 kg cat sitting motionless on rug

Fg (E, C)

Fn (R, C)

Fg = 5 kg x 10 m/s2

Fg = 50 N

Fn = 50 N (must balance Fg)

50 N

50 N

With 1-D forces, it’s fairly easy

With 2-D forces, we have to do a bit more work to calculate the forces involved• Involves basic trigonometry

First, a little intro to basic trig.

Sine, Cosine, and Tangent• 3 main functions in trig• Usually shortened as sin, cos, and tanTo calculate sin, cos, and tan• Divide the length of one side by

another side……but you must know which sides!

SOH CAH TOA

Find the height of the flag pole and the hypotenuse

Find the hypotenuse and the length of the side adjacent (next to) the angle given

Let’s apply what we have just learned to a more physics-based question:• An 10 kg object sits motionless on an

incline due to friction

300

The 2000 kg elephant is standing motionless on the ramp due to friction.• What is the normal force that the ramp is

pushing up on the elephant with?

What is the force of friction that prevents the elephant from sliding down?