Exercise: Trigonometry 2

5.5.2. Exercise: Trigonometry 2#

When we walk on an inclined treadmill as in Fig. 5.7, we must overcome a backward force that is equal to:

\[ F = m g \sin \theta \]

where \(m\) is the person’s mass, \(g\) is 9.81 m/s² and \(\theta\) is the treadmill angle. Write a function names plot_force that takes the mass as an argument, and that plots \(F\) for \(\theta \in [-20, 20]\) degrees. Then, test your function for \(m = 65\) kg.

Fig. 5.7 Walking on an inclined surface.#

Hide code cell content
import numpy as np
import matplotlib.pyplot as plt


def plot_force(m: float) -> None:
    """
    Plot the force a persons need to overcome on an inclined treadmill.

    Parameters
    ----------
    m :
        Mass of the person in kilograms

    Returns
    -------
    None

    """
    # First, let's define an angle array
    theta = np.linspace(-30, 30, 100, endpoint=False)

    # Calculate the force
    force = m * 9.81 * np.sin(np.deg2rad(theta))

    # Plot it
    plt.plot(theta, force)
    plt.xlabel("Angle (deg)")
    plt.ylabel("Force (N)")
    plt.show()


# Test the function
plot_force(65)
_images/66cb184e3e4a281aab96d7f11d78c7ceb3055b3cc0535d65f460ea6b783fab28.png