Question

in physics lab, latanya attaches a wireless sensor to one of the spokes of a bicycle wheel spinning freely on its axle. the graph below shows the sensors height above the ground, in centimeters, over time t, measured in seconds. what is the amplitude and what does it represent in this context?

Explanation:

Step1: Identify maximum and minimum

The maximum height values are 47 cm (at \(t = 0.5\) s and \(t=4.5\) s) and the minimum height values are 33 cm (at \(t = 2.5\) s and \(t = 6.5\) s).

Step2: Calculate the amplitude formula

The amplitude \(A\) of a periodic - function is given by \(A=\frac{\text{Max}-\text{Min}}{2}\).

Step3: Substitute values

Substitute Max = 47 cm and Min = 33 cm into the formula: \(A=\frac{47 - 33}{2}=\frac{14}{2}=7\) cm.

Step4: Interpret the amplitude

In this context, the amplitude represents the maximum displacement of the sensor from its equilibrium (average) height as the bicycle wheel spins. The equilibrium height is \(\frac{47 + 33}{2}=40\) cm, and the amplitude of 7 cm means the sensor moves up and down 7 cm from this equilibrium position as the wheel rotates.

Answer:

The amplitude is 7 cm. It represents the maximum displacement of the sensor from its equilibrium height as the bicycle wheel spins.