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Chapter 8: Problem 17

Is it possible for two masses to undergo a collision such that the system of two masses has more kinetic energy than the two separate masses had? Explain.

Short Answer

Expert verified
Answer: No, it is not possible for two masses to undergo a collision and have more kinetic energy afterward than the two separate masses had before the collision. Both elastic and inelastic collisions cannot result in a system with an increase in total kinetic energy.

Step by step solution

01

Understand types of collisions and conservation of energy

In physics, collisions can be categorized into two types: elastic and inelastic. In an elastic collision, both kinetic energy and momentum are conserved. In an inelastic collision, only momentum is conserved, while kinetic energy is not. The principle of conservation of energy states that the total energy of an isolated system remains constant, meaning that energy cannot be created nor destroyed, only transformed.
02

Analyze elastic collisions

In an elastic collision, both momentum and kinetic energy are conserved. This means that the total kinetic energy of the system (the two colliding masses) before and after the collision remains the same. Thus, for elastic collisions, it is not possible for the system of two masses to have more kinetic energy after the collision than the two separate masses had initially.
03

Analyze inelastic collisions

In an inelastic collision, only momentum is conserved, while kinetic energy is not. This means that some of the initial kinetic energy will be transformed into other forms of energy (e.g., internal, potential, or sound energy) during the collision. Consequently, the total kinetic energy of the system after the collision will always be less than the total kinetic energy of the two separate masses before the collision. As a result, it is not possible for the system of two masses to have more kinetic energy after an inelastic collision than the two separate masses had initially.
04

Conclusion

After analyzing both types of collisions, it becomes evident that it is not possible for two masses to undergo a collision and have more kinetic energy afterward than the two separate masses had before the collision. Both elastic and inelastic collisions cannot result in a system with an increase in total kinetic energy.

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Most popular questions from this chapter

A toy car of mass \(2.0 \mathrm{~kg}\) is stationary, and a child rolls a toy truck of mass 3.5 kg straight toward it with a speed of \(4.0 \mathrm{~m} / \mathrm{s}\) a) What is the velocity of the center of mass of the system consisting of the two toys? b) What are the velocities of the truck and the car with respect to the center of mass of the system consisting of the two toys?

Find the center of mass of a rectangular plate of length \(20.0 \mathrm{~cm}\) and width \(10.0 \mathrm{~cm} .\) The mass density varies linearly along the length. At one end, it is \(5.00 \mathrm{~g} / \mathrm{cm}^{2}\); at the other end, it is \(20.0 \mathrm{~g} / \mathrm{cm}^{2}\)

One important characteristic of rocket engines is the specific impulse, which is defined as the total impulse (time integral of the thrust) per unit ground weight of fuel/oxidizer expended. (The use of weight, instead of mass, in this definition is due to purely historical reasons.) a) Consider a rocket engine operating in free space with an exhaust nozzle speed of \(v\). Calculate the specific impulse of this engine. b) A model rocket engine has a typical exhaust speed of \(v_{\text {toy }}=800 . \mathrm{m} / \mathrm{s}\). The best chemical rocket engines have exhaust speeds of approximately \(v_{\text {chem }}=4.00 \mathrm{~km} / \mathrm{s} .\) Evaluate and compare the specific impulse values for these engines.

An astronaut is performing a space walk outside the International Space Station. The total mass of the astronaut with her space suit and all her gear is \(115 \mathrm{~kg} .\) A small leak develops in her propulsion system and \(7.00 \mathrm{~g}\) of gas are ejected each second into space with a speed of \(800 \mathrm{~m} / \mathrm{s}\). She notices the leak 6.00 s after it starts. How much will the gas leak have caused her to move from her original location in space by that time?

The distance between a carbon atom \((m=12 \mathrm{u})\) and an oxygen atom \((m=16 \mathrm{u})\) in a carbon monoxide \((\mathrm{CO})\) molecule is \(1.13 \cdot 10^{-10} \mathrm{~m} .\) How far from the carbon atom is the center of mass of the molecule? \((1 \mathrm{u}=1\) atomic mass unit. \()\)
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