Part 1
In the 1950’s, an experimental train that had a mass of 32800 kg was powered across a level track by a jet engine that produced a thrust of 4.37 × 10^5N for a distance of 465 m.
Find the work done on the train.
Answer in units of J.
Part 2
Find the change in kinetic energy.
Answer in units of J.
Part 3
Find the final kinetic energy of the train if it
started from rest.
Answer in units of J.
Part 4
Find the final speed of the train assuming no
friction.
Answer in units of m/s.
A) Start with the definition of Work.
Force x Distance
B) Work = change in KE. This assumes negligible friction. They should have told you a value to assume for friction, or to neglect it.
C) Same as B
D) Use KE definition to get V. The "no friction assumption" had to be made already, in B. This problem was not well thought out by the instructor
Part 1: To find the work done on the train, we can use the formula:
Work = Force x Distance
In this case, the force is the thrust of the jet engine, which is 4.37 × 10^5 N, and the distance is 465 m. Plugging in these values, we can calculate the work done on the train:
Work = (4.37 × 10^5 N) x (465 m)
Work = 2.0335 x 10^8 J
Therefore, the work done on the train is approximately 2.0335 x 10^8 J.
Part 2: The change in kinetic energy can be calculated using the work-energy theorem, which states that the work done on an object is equal to the change in its kinetic energy.
Change in Kinetic Energy = Work
Using the value of work we calculated in Part 1, we can say:
Change in Kinetic Energy = 2.0335 x 10^8 J
Therefore, the change in kinetic energy is approximately 2.0335 x 10^8 J.
Part 3: The final kinetic energy of the train, assuming it started from rest, can be found by adding the change in kinetic energy to the initial kinetic energy. Since the train starts from rest, its initial kinetic energy is 0.
Final Kinetic Energy = Initial Kinetic Energy + Change in Kinetic Energy
Final Kinetic Energy = 0 + 2.0335 x 10^8 J
Therefore, the final kinetic energy of the train is approximately 2.0335 x 10^8 J.
Part 4: Assuming no friction, we can use the kinetic energy formula to find the final speed of the train. The kinetic energy formula is:
Kinetic Energy = (1/2) x mass x velocity^2
Rearranging the formula, we can solve for velocity:
velocity = sqrt(2 x Kinetic Energy / mass)
Plugging in the values of the final kinetic energy (2.0335 x 10^8 J) and the mass of the train (32800 kg), we can calculate the final speed:
velocity = sqrt(2 x (2.0335 x 10^8 J) / (32800 kg))
velocity ≈ 101.09 m/s
Therefore, the final speed of the train, assuming no friction, is approximately 101.09 m/s.