The most massive of the shikansen are the series 200 trains, yet they are among the fastest. Series 200 trains can reach speeds of 275 km/h. If a 16-car series 200 trains has a maximum kinetic energy of 2.78 x 10^9 J, what is its mass?
Kinetic energy = 1/2 m (v^2)
you know the KE and the speed
(have to convert km/h into m/s)
find the "m" using the formula
5.93 X 10^5 kg
To find the mass of the 16-car series 200 train, we can use the equation for kinetic energy:
Kinetic Energy (KE) = (1/2) * mass * velocity^2
Given that the kinetic energy is 2.78 x 10^9 J and the velocity is 275 km/h (which can be converted to m/s), we can solve for the mass.
Step 1: Convert the velocity from km/h to m/s.
Given: Velocity = 275 km/h
Conversion: 1 km/h = 0.2778 m/s (approx.)
Velocity = 275 km/h * 0.2778 m/s = 76.17 m/s (approx.)
Step 2: Plug the values into the equation for kinetic energy.
Given: KE = 2.78 x 10^9 J, Velocity = 76.17 m/s
KE = (1/2) * mass * velocity^2
2.78 x 10^9 J = (1/2) * mass * (76.17 m/s)^2
Step 3: Solve for the mass.
Divide both sides of the equation by (1/2) * (76.17 m/s)^2.
(2.78 x 10^9 J) / [(1/2) * (76.17 m/s)^2] = mass
mass ≈ 194,383 kg
Therefore, the mass of the 16-car series 200 train is approximately 194,383 kg.