In the 1950s, an experimental train that had a mass of 3.30 104 kg was powered across level track by a jet engine that produced a thrust of 4.90 105 N for a distance of 600 m.
(a) Find the work done on the train.
1 J
(b) Find the change in kinetic energy.
2 J
(c) Find the final kinetic energy of the train if it started from rest.
3 J
(d) Find the final speed of the train if there was no friction.
4 m/s
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1) Work = force • distance
Work = F•s = 4.9•105•600 =2.94•10^8 J.
2) work done = energy gained
Kinetic energy gained = 2.94•10^8 J It had 0 KÓ to start, so this is its change in KE.
3) This is also the final KE of the train.
4) KE = m•v²/2.
2.94•10^8 = 0.5•3.3•10^4• v².
V = sqrt (2.94•10^8/0.5•3.3•10^4) = 133.5 m/s
To find the answers to the given questions, we need to use some formulas and concepts related to work, kinetic energy, and Newton's laws of motion. Let's go step by step:
(a) To find the work done on the train, we can use the formula:
Work = Force x Distance
Given:
Force (F) = 4.90 x 10^5 N (thrust produced by the jet engine)
Distance (d) = 600 m
Substituting the values into the formula, we get:
Work = (4.90 x 10^5 N) x (600 m)
= 2.94 x 10^8 J
So, the work done on the train is 2.94 x 10^8 Joules.
(b) To find the change in kinetic energy, we can use the work-energy theorem, which states that the work done on an object is equal to the change in its kinetic energy. The formula to calculate the change in kinetic energy is:
Change in Kinetic Energy = Work
Using the value of work from part (a), we have:
Change in Kinetic Energy = 2.94 x 10^8 J
Therefore, the change in kinetic energy is 2.94 x 10^8 Joules.
(c) To find the final kinetic energy of the train if it started from rest, we need to calculate the initial kinetic energy and add it to the change in kinetic energy found in part (b). The initial kinetic energy of an object at rest is zero. Therefore, the final kinetic energy would be:
Final Kinetic Energy = Initial Kinetic Energy + Change in Kinetic Energy
= 0 + 2.94 x 10^8 J
Hence, the final kinetic energy of the train is 2.94 x 10^8 Joules.
(d) To find the final speed of the train if there was no friction, we can use the kinetic energy formula:
Kinetic Energy = 1/2 x Mass x Velocity^2
Given:
Mass (m) = 3.30 x 10^4 kg
Final Kinetic Energy = 2.94 x 10^8 J
Rearranging the formula, we get:
Velocity^2 = (2 x Final Kinetic Energy) / Mass
= (2 x 2.94 x 10^8 J) / (3.30 x 10^4 kg)
Simplifying the equation, we have:
Velocity^2 = 1.78 x 10^4 m^2/s^2
Taking the square root of both sides, we get:
Velocity = √(1.78 x 10^4) m/s
= 133.43 m/s (approximately)
Therefore, the final speed of the train, if there was no friction, would be approximately 133.43 m/s.
In summary:
(a) The work done on the train is 2.94 x 10^8 Joules.
(b) The change in kinetic energy is 2.94 x 10^8 Joules.
(c) The final kinetic energy of the train is 2.94 x 10^8 Joules.
(d) The final speed of the train, if there was no friction, is approximately 133.43 m/s.