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Understanding Predictive Power in 2-D Forces Using Free Body Diagrams and Trigonometry

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In this lesson, we explore the predictive power of Free Body Diagrams (FBDs) in the context of two-dimensional forces. Building on concepts from units 1 and 2, we emphasize the importance of concrete numerical predictions in physics, such as calculating velocity and distance. Using basic trigonometry, we calculate forces acting on objects, exemplified by a 5 kg cat and a 10 kg object on an incline. We illustrate the applications of sine, cosine, and tangent in determining the normal force and frictional forces, enhancing our understanding of motion in two dimensions.

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Understanding Predictive Power in 2-D Forces Using Free Body Diagrams and Trigonometry

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  1. Quantitative FBDs • Just 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 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 Fn (R, C) 5 kg cat sitting motionless on rug 50 N 50 N Fg = 5 kg x 10 m/s2 Fg = 50 N Fn = 50 N (must balance Fg) Fg (E, C)

  2. First, a little intro to basic trig. • Sine, Cosine, and Tangent • 3 main functions in trig • Usually shortened as sin, cos, and tan SOH CAH TOA • To calculate sin, cos, and tan • Divide the length of one side by another side……but you must know which sides!

  3. Find the height of the flag pole and the hypotenuse

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

  5. 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

  6. 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?

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