Question

A train of mass 2.4x10⁶ kg enters a 5.0 km stretch of track with a vertical rise of 40 m at a speed of 1.0 m/s and leaves at 3.0 m/s. Assuming that frictional drag is negligible:

Define and find a value for each term in the equation Wnc=ΔK+ΔU.

Answer 1

The equation Wnc = ΔK + ΔU represents the work-energy theorem, which states that the net work done on an object is equal to the change in its kinetic energy and potential energy. To find the values for each term in the equation, we need to calculate the initial and final kinetic energies and potential energies of the train.

Step-by-step explanation:

The equation Wnc = ΔK + ΔU represents the work-energy theorem, which states that the net work done on an object is equal to the change in its kinetic energy and potential energy. In this equation:

Wnc

represents the net work done on the object,

ΔK

represents the change in kinetic energy, and

ΔU

represents the change in potential energy. To find the values for each term, we need to calculate the initial and final kinetic energies and potential energies of the train.

1. Initial kinetic energy: K_i = 0.5mv_i^2
2. Final kinetic energy: K_f = 0.5mv_f^2
3. Initial potential energy: U_i = mgh_i
4. Final potential energy: U_f = mgh_f

Now we can substitute these values into the equation: Wnc = (K_f - K_i) + (U_f - U_i).