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.
J
(b) Find the change in kinetic energy.
J
(c) Find the final kinetic energy of the train if it started from rest.
J
(d) Find the final speed of the train if there was no friction.
1) Work = force • distance
Work = F2•3s = 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 Ke 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 questions, we need to apply the formulas for work and kinetic energy.
(a) The work done on an object is given by the formula:
Work = Force * Distance
In this case, the force is the thrust produced by the jet engine, which is 4.90 * 10^5 N, and the distance traveled is 600 m. Plugging the values into the formula:
Work = (4.90 * 10^5 N) * (600 m) = 2.94 * 10^8 J
Therefore, the work done on the train is 2.94 * 10^8 J.
(b) The change in kinetic energy of an object is given by the formula:
ΔKE = Work
Since we already calculated the work done on the train to be 2.94 * 10^8 J, the change in kinetic energy is also 2.94 * 10^8 J.
(c) To find the final kinetic energy of the train if it started from rest, we can use the formula for kinetic energy:
KE = (1/2) * mass * velocity^2
Since the train starts from rest, its initial kinetic energy is zero. Therefore, the final kinetic energy is equal to the change in kinetic energy:
Final KE = Change in KE = 2.94 * 10^8 J
(d) To find the final speed of the train if there was no friction, we can rearrange the formula for kinetic energy as follows:
KE = (1/2) * mass * velocity^2
Rearranging the equation:
velocity^2 = (2 * KE) / mass
Plugging in the values for final KE and mass (3.30 * 10^4 kg):
velocity^2 = (2 * (2.94 * 10^8 J)) / (3.30 * 10^4 kg)
Simplifying the equation:
velocity^2 = 1.77 * 10^4 m^2/s^2
Taking square root of both sides to find velocity:
velocity = sqrt(1.77 * 10^4 m^2/s^2)
Therefore, the final speed of the train, without considering friction, is approximately equal to 133 m/s.