An experimental train has a mass of 1.70e4 kg and is powered across a level track by a jet engine that produces a thrust of 4.90e5 N for a distance of 520 m. a) Find the change in kinetic energy. b) Find the final kinetic energy of the train if it started from rest. c) Find the final speed of the train if there was no friction.
My thoughts: KE = 1/2(m)(v^2). The change in kinetic energy would be the mass of the train times some velocity. But how would you find the velocity?
Equate that with force*distance. you are given both.
To find the velocity of the train, you can use Newton's second law of motion, which states that force is equal to mass multiplied by acceleration. In this case, the force is the thrust produced by the jet engine and the mass is the mass of the train.
a) To find the change in kinetic energy, we can use the work-energy principle, which states that the work done on an object is equal to the change in its kinetic energy.
Since work done is equal to force multiplied by the distance, we can use this formula to calculate the change in kinetic energy:
Change in kinetic energy = Work done = Force × Distance
Given:
Mass of the train (m) = 1.70e4 kg
Thrust produced by the jet engine (F) = 4.90e5 N
Distance traveled (d) = 520 m
Using Newton's second law of motion, we can find the acceleration (a) of the train:
Force = mass × acceleration
4.90e5 N = 1.70e4 kg × a
Solving for a, we can find that acceleration is equal to (4.90e5 N) / (1.70e4 kg).
Now, we can calculate the change in kinetic energy using the work-energy principle:
Change in kinetic energy = Force × Distance
Change in kinetic energy = (4.90e5 N) × (520 m)
b) To find the final kinetic energy of the train if it started from rest, we need to consider that the initial kinetic energy is zero.
So, the final kinetic energy would be equal to the change in kinetic energy calculated in part a.
c) To find the final speed of the train if there was no friction, we can use the formula for kinetic energy:
Final kinetic energy = 1/2 × mass × final velocity^2
Since the initial velocity is zero, the change in kinetic energy calculated in part a is equal to the final kinetic energy. We can equate this value to the formula for kinetic energy:
Change in kinetic energy = 1/2 × mass × final velocity^2
Now, solve the equation for the final velocity of the train square-rooting both sides:
Final velocity = square root of (2 × Change in kinetic energy) / mass
Use the calculated change in kinetic energy and the mass of the train to find the final velocity.