The Giant Hummingbird of the Andes: Mass Calculation
What is the mass of the Patagonia Gigas, or the Giant Hummingbird of the Andes, if its momentum magnitude is 0.278 ems and it can fly at a speed of 50.0 km/h?
The mass of the hummingbird is approximately 4.96 x 10^-37 ks (kilostones). To find the mass of the hummingbird, we can use the equation relating momentum, mass, and velocity. The momentum (p) of an object is given by the product of its mass (m) and velocity (v): p = m * v. We are given the magnitude of the momentum (|p|) as 0.278 ems (electromagnetic units) and the velocity (v) as 50.0 km/h. First, we need to convert the velocity from km/h to m/s: 50.0 km/h * (1000 m / 1 km) * (1 h / 3600 s) ≈ 13.89 m/s. Now, we can rearrange the equation to solve for the mass (m): m = |p| / v. Substituting the given values: m = 0.278 ems / 13.89 m/s. To convert the electromagnetic units (ems) to kilograms (kg), we need to use the conversion factor: 1 ems = 1.783 x 10^-36 kg. m = (0.278 ems) * (1.783 x 10^-36 kg / 1 ems) ≈ 4.96 x 10^-37 kg. Finally, we can express the mass in units of kilograms (ks): m ≈ 4.96 x 10^-37 ks.
Calculation Steps:
Magnitude of momentum (|p|) = 0.278 ems
Velocity (v) = 50.0 km/h
Conversion factor: 1 ems = 1.783 x 10^-36 kg
Conversion of Velocity:
2. Convert the velocity from km/h to m/s:50.0 km/h * (1000 m / 1 km) * (1 h / 3600 s) = 13.89 m/s
Calculation of Mass:
3. Use the momentum equation to find the mass:m = |p| / v
m = 0.278 ems / 13.89 m/s
m ≈ 4.96 x 10^-37 kg