Final answer:
To calculate the velocity of the end of a vibrating steel strip at the zero position, convert the amplitude to meters and use the formula for velocity in simple harmonic motion. With an amplitude of 5mm and a frequency of 20Hz, the maximum velocity at the zero position is 0.2π m/s.
Step-by-step explanation:
The question asks us to calculate the velocity of the end of a steel strip when passing through the zero position. Based on the information given, the steel strip is vibrating with a frequency of 20Hz, and the amplitude of the vibration is 5mm. The velocity at the zero position, which is the point of maximum speed, can be calculated using the formula for the velocity (v) of an object in simple harmonic motion: v = A⋅ω, where A is the amplitude, and ω (omega) is the angular frequency.
First, we convert the amplitude from millimeters to meters: A = 5mm = 0.005m. Then we determine the angular frequency: ω = 2⋅π⋅f, where f is the frequency. Plugging into the equation, we get ω = 2⋅π⋅20Hz = 40π rad/s. Thus, the maximum velocity at the zero position can be calculated as: Vmax = 0.005m ⋅ 40π rad/s = 0.2π m/s.