A bicep muscle shown in Fig. P2.3 can apply a force F measured in Newtons (N) as a function of the elbow angle ϕ, measured in degrees as described by the quadratic equation F(ϕ) = 6ϕ − 0.04ϕ2. For a bicep force of F = 200 N, solve the equation for ϕ by each of the following methods: factoring, completing the square, and the quadratic formula. Using your solution from part (a), determine the elbow angle ϕ where the force exerted by the bicep is maximum. In addition, calculate the maximum force Fmax.

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A bicep muscle shown in Fig. P2.3 can apply a force F measured in Newtons (N) as a function of the elbow angle ϕ, measured in degrees as described by the quadratic equation F(ϕ) = 6ϕ − 0.04ϕ2.

  1. For a bicep force of F = 200 N, solve the equation for ϕ by each of the following methods: factoring, completing the square, and the quadratic formula.
  2. Using your solution from part (a), determine the elbow angle ϕ where the force exerted by the bicep is maximum. In addition, calculate the maximum force Fmax.
  3. Plot F versus ϕ and clearly indicate the maximum force on the graph. Also clearly label the x-intercepts on the graph.
Ф
> F
Transcribed Image Text:Ф > F
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What is the graph? (part c)

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