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Chapter 28: Q20CQ (page 1028)

We know that the velocity of an object with mass has an upper limit of c. Is there an upper limit on its momentum? Its energy? Explain.

Short Answer

Expert verified

There is no upper limit to momentum or energy.

Step by step solution

01

Definition of mass and momentum 

The quantity of matter in a physical body is referred to as its mass. It is also used to calculate the body's inertia, or resistance to acceleration when a net force is applied.

The term "momentum" refers to "mass in motion." Because all objects have mass, if an object is moving, it has momentum.

02

Explanation

Since it is a relativistic particle, the momentum is given by the following equation:\({\rm{p = \gamma mv}}\), and that neither\(\gamma \)nor\(m\)has an upper limit, then there is no upper limit for the momentum.

Meanwhile, the energy given by \(E = m{c^2}\) has no upper limit because \(m\) can be any value.

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Most popular questions from this chapter

(a) Show that\[{\left({pc}\right)^2}/{\left({m{c^2}{\rm{}}} \right)^2}{\rm{ }} = {\rm{ }}{\gamma ^2}{\rm{ }} - {\rm{ }}1\]. This means that at large velocities\[pc>>m{c^2}\]. (b) Is\[E{\rm{}}\approx{\rm{}}pc\]when\[\gamma{\rm{}}={\rm{}}30.0\], as for the astronaut discussed in the twin paradox?

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