In the 1950s, an experimental train that had a mass of 2.65 104 kg was powered across a level track by a jet engine that produced a thrust of 5.25 105 N for a distance of 509 m. Assume that air resistance is negligible.
(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 had been no friction.
m/s____
(b) Work done = Force x distance
(c) same as (b)
(d) sqrt [2*(K.E)*M]
There is an error in the form for question (d)
vf = sqrt [2*(K.E)/M]
To find the change in kinetic energy, we can use the formula:
Change in kinetic energy (ΔK) = Final kinetic energy (Kf) - Initial kinetic energy (Ki)
To find the final kinetic energy of the train, we can use the formula:
Final kinetic energy (Kf) = 1/2 * mass * (final velocity)^2
To find the final speed of the train, we can use the equation:
Final speed (v) = √[(2 * kinetic energy) / mass]
Let's solve each part of the question step by step.
(b) Find the change in kinetic energy:
First, we need to find the initial kinetic energy (Ki). Since the train started from rest, it has zero initial kinetic energy.
Ki = 0
Now, let's find the final kinetic energy (Kf):
Kf = 1/2 * mass * (final velocity)^2
The mass of the train is given as 2.65 * 10^4 kg.
The final velocity is not given directly, but we can calculate it using Newton's second law:
Thrust (F) = mass * acceleration
Since there is no friction, the net force acting on the train is equal to the thrust of the jet engine.
F = 5.25 * 10^5 N
From the equation F = mass * acceleration, rearranging for acceleration:
acceleration = F / mass
Now, we can use the equation of motion:
(final velocity)^2 = (initial velocity)^2 + 2 * acceleration * distance
Since the train started from rest, the initial velocity is zero.
(final velocity)^2 = 2 * acceleration * distance
Plug in the values:
(final velocity)^2 = 2 * (F / mass) * distance
Now, calculate the final velocity:
final velocity = √[(2 * (F / mass) * distance)]
Now, use the final velocity to calculate the final kinetic energy:
Kf = 1/2 * mass * (final velocity)^2
Plug in the values:
Kf = 1/2 * (mass) * (final velocity)^2
Calculate the final kinetic energy.
(c) Find the final kinetic energy of the train if it started from rest:
Using the formula for final kinetic energy:
Final kinetic energy (Kf) = 1/2 * mass * (final velocity)^2
Since the train started from rest, its initial kinetic energy is zero.
Kf = Final kinetic energy
Calculate the final kinetic energy.
(d) Find the final speed of the train if there had been no friction:
Using the equation for final speed:
Final speed (v) = √[(2 * kinetic energy) / mass]
Calculate the final speed.
I hope this explanation helps you understand how to solve the problem!