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Chapter 5: Problem 17

Two railroad cars, each of mass \(7000 . \mathrm{kg}\) and traveling at \(90.0 \mathrm{~km} / \mathrm{h},\) collide head on and come to rest. How much mechanical energy is lost in this collision?

Short Answer

Expert verified
Answer: The mechanical energy lost during the collision is 1750000 J (joules).

Step by step solution

01

Convert velocities to m/s

First, we need to convert the given velocities from km/h to m/s for both railroad cars. To do this, we can use the conversion factor 1 km/h = (1000 m/km) / (3600 s/h). Multiply the given velocity (90.0 km/h) by this conversion factor: Velocity_car1 = Velocity_car2 = 90.0 km/h × (1000 m/km) / (3600 s/h) = 25.0 m/s
02

Calculate the initial and final momentum of the system

Before the collision, each car has an equal and opposite momentum (since they have equal masses and velocities). The initial momentum of the system is the sum of the momentums of both cars, while the final momentum of the system is zero (since they come to rest after the collision). Initial_momentum = Mass_car1 × Velocity_car1 - Mass_car2 × (-Velocity_car2) = 7000 kg × 25.0 m/s + 7000 kg × 25.0 m/s = 350000 kg m/s Final_momentum = 0 kg m/s (since both cars come to rest)
03

Calculate the initial and final kinetic energy of the system

Calculate the initial kinetic energy (KE) of the system as the sum of the kinetic energies of both cars. Then calculate the final kinetic energy of the system, which is zero (since the cars come to rest). Initial_KE = 0.5 × Mass_car1 × Velocity_car1^2 + 0.5 × Mass_car2 × (-Velocity_car2)^2 = 0.5 * 7000 kg × (25.0 m/s)^2 + 0.5 × 7000 kg × (25.0 m/s)^2 = 1750000 J Final_KE = 0 J (since both cars come to rest)
04

Calculate the mechanical energy lost during the collision

The mechanical energy lost in the collision is equal to the difference between the initial kinetic energy and the final kinetic energy. Mechanical_energy_lost = Initial_KE - Final_KE = 1750000 J - 0 J = 1750000 J Therefore, the mechanical energy lost during the collision is 1750000 J (joules).

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