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Chapter 33: Problem 53

Find (a) the speed and (b) the momentum of a proton with kinetic energy \(500 \mathrm{MeV}.\)

Short Answer

Expert verified
The speed and the momentum of a proton with kinetic energy \(500 MeV\).

Step by step solution

01

Recall the Kinetic Energy formula

The formula for kinetic energy is given by \(KE = \frac{1}{2}mv^2\) where \(m\) is the mass of the object and \(v\) is its velocity. Here, \(KE = 500 MeV = 500 \times 10^6 \times 1.6 \times 10^{-19} J\), and the mass of a proton is \(m = 1.67 \times 10^{-27} kg\). Solve this equation for \(v\) to compute the speed.
02

Compute the speed

After rearranging the equation for speed, it becomes \(v = \sqrt{\frac{2KE}{m}}\). Substituting the given values, compute the speed of the proton.
03

Recall the momentum formula

The momentum of a particle is given by \(p=mv\). We can use the speed obtained in step 2 to find the momentum.
04

Compute the momentum

Substitute the mass of the proton and the speed calculated in step 2 into the momentum formula to find the momentum of the proton.

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Most popular questions from this chapter

You've been named captain of NASA's first interstellar mission since the Voyager robotic spacecraft. You board your spaceship, accelerate quickly to \(0.8 c,\) and cruise at constant speed toward Proxima Centauri, the closest star to our Sun. Proxima Centauri is 4 light-years distant as measured in the two stars' common rest frame. On the way, you conduct various medical experiments to determine the effects of a long space voyage on the human body. Taking your pulse, you find a. it's significantly slower than when you're on Earth. b. it's the same as when you're on Earth. c. it's significantly faster than when you're on Earth.

A particle is moving at \(0.90 c .\) If its speed increases by \(10 \%,\) by what factor does its momentum increase?

At what speed will the momentum of a proton (mass 1 \(\mathrm{u}\) ) equal that of an alpha particle (mass 4 u) moving at \(0.5 c ?\)

Find the kinetic energy of an electron moving at (a) \(0.0010 c\) (b) \(0.60 c,\) and \((\mathrm{c}) 0.99 c .\) Use suitable approximations where possible.

How fast would you have to go to reach a star 200 light years away in a 75 -year human lifetime?
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