In 1896 in Waco, Texas, William Crush of the “ Katy” railroad parked two locomotives at opposite ends of a 6.4 km track, fired them up, tied their throttles open, and then allowed them to crash head-on at full speed in front of 30,000 spectators. Hundreds were hurt by flying debris; several were killed. Assuming the weight of each locomotive was 1.2 x 10^6 N and its acceleration prior to the collision was a constant 0.26 m/s^2, what was the total

kinetic energy of the two locomotives just before the collision?

V1 = V2.

d1 = d2 = 6.4km/2 = 3.2 km before collision.
M*g = 1.2*10^6, M = 1.2*10^6/9.8 = 1.22*10^5 kg.

V^2 = Vo^2 + 2a*d.
V^2 = 0 + 0.52*3200
V = 40.8 m/s. = Velocity before collision.

KE = 2(M*V^2/2) = M*V^2.

good, very good.Danke

To calculate the total kinetic energy of the two locomotives just before the collision, we can use the formula for kinetic energy:

Kinetic Energy = 0.5 * mass * velocity^2

Since the problem provides the weight of each locomotive, we can use this information to find the mass of each locomotive using the formula:

Weight = mass * acceleration due to gravity

Given:
Weight of each locomotive = 1.2 x 10^6 N
Acceleration due to gravity = 9.8 m/s^2

Step 1: Find the mass of each locomotive
We can rearrange the formula to solve for mass:

mass = weight / acceleration due to gravity

Let's calculate the mass of each locomotive:

Locomotive 1:
mass1 = (1.2 x 10^6 N) / (9.8 m/s^2)

Locomotive 2:
mass2 = (1.2 x 10^6 N) / (9.8 m/s^2)

Step 2: Find the velocity of each locomotive
We are given the acceleration prior to the collision, which we can assume to be constant. We also know that the distance covered by each locomotive before the collision is 6.4 km.

Using the equation for motion:

velocity^2 = initial velocity^2 + 2 * acceleration * distance

Since the initial velocity is 0, we can simplify the equation to:

velocity^2 = 2 * acceleration * distance

Let's calculate the velocity of each locomotive before the collision:

Locomotive 1:
velocity1^2 = 2 * (0.26 m/s^2) * (6.4 km)

Locomotive 2:
velocity2^2 = 2 * (0.26 m/s^2) * (6.4 km)

Step 3: Calculate the kinetic energy of each locomotive
Now that we have the mass and velocity of each locomotive, we can calculate their kinetic energy using the formula mentioned earlier:

Kinetic Energy = 0.5 * mass * velocity^2

Let's calculate the kinetic energy of each locomotive:

Kinetic energy1 = 0.5 * mass1 * velocity1^2

Kinetic energy2 = 0.5 * mass2 * velocity2^2

Step 4: Find the total kinetic energy
To find the total kinetic energy of the two locomotives just before the collision, we can add the individual kinetic energies together:

Total Kinetic Energy = Kinetic energy1 + Kinetic energy2

Now you can substitute the given values and perform the calculations to find the total kinetic energy.

To find the total kinetic energy of the two locomotives just before the collision, we can use the formula for kinetic energy:

Kinetic Energy = (1/2) * mass * velocity^2

First, we need to find the velocity of each locomotive just before the collision. We can do this using the formula for acceleration:

acceleration = (change in velocity) / time

Rearranging the formula, we get:

(change in velocity) = acceleration * time

Given that the acceleration is 0.26 m/s^2, we need to determine the time it takes for the locomotives to reach their final velocities before the collision. We do not have the specific time mentioned in the question, so we cannot calculate the exact final velocity. Instead, we will consider the final velocity reached after a certain time, which will be sufficient for calculating the initial kinetic energy.

Now, we calculate the change in velocity by multiplying the acceleration by the time:

(change in velocity) = 0.26 m/s^2 * (time in seconds)

Next, we can equate the change in velocity with the final velocity (approximately):

(change in velocity) = (final velocity - initial velocity)

Now, let's assume the initial velocity is 0 m/s (the locomotives start from rest) and the final velocity is the velocity reached after a certain time. We will consider the final velocity as v (in m/s).

Therefore, the change in velocity equals v - 0, which simplifies to v.

Equating this with the expression for change in velocity, we get:

v = 0.26 m/s^2 * (time in seconds)

To find the time in seconds, we need additional information or assumptions. Since the question doesn't provide it, we cannot calculate the exact final velocity or kinetic energy. However, you can assume a reasonable value for time (in seconds) and proceed with the calculations.

Once you have the final velocity (v), the mass (m) of each locomotive (given as 1.2 x 10^6 N, which represents the weight), and assuming the initial velocity is 0 m/s, you can calculate the kinetic energy of each locomotive using the formula:

Kinetic Energy = (1/2) * mass * velocity^2

After finding the kinetic energy of each locomotive, you can add them together to find the total kinetic energy just before the collision.