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Chapter 26: Problem 33

A proton moves at \(0.90 c .\) What is its momentum in \(\mathrm{SI}\) units?

Short Answer

Expert verified
Answer: The momentum of the proton moving at 0.90c is approximately \(4.509 \times 10^{-19}\) kg m/s.

Step by step solution

01

Identify the given information and the required constants

We are given the velocity of the proton (\(0.90 c\)) and are asked to find its momentum. We need the mass of a proton and the speed of light (in SI units) as additional information. - Proton mass (m) = \(1.67 \times 10^{-27}\) kg - Speed of light (c) = \(3.00 \times 10^8\) m/s
02

Calculate the velocity of the proton

The proton is moving at \(0.90 c\), so its velocity (v) can be calculated using the following formula: \(v = 0.90 \times c\) \(v = 0.90 \times 3.00 \times 10^8\) m/s Plug in the value of the speed of light and perform the multiplication to find the velocity of the proton: \(v = 2.70 \times 10^8\) m/s
03

Calculate the momentum of the proton

Now that we have the mass of a proton (m) and its velocity (v), we can calculate its momentum (p) using the formula: \(p = mv\) Plug in the values for mass and velocity and perform the multiplication: \(p = (1.67 \times 10^{-27} \text{ kg})(2.70 \times 10^8 \text{ m/s})\)
04

Calculate the momentum in SI units

Multiply the mass and velocity together: \(p = 4.509 \times 10^{-19}\) kg m/s The momentum of the proton moving at \(0.90c\) is approximately \(4.509 \times 10^{-19}\) kg m/s in SI units.

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Most popular questions from this chapter

A rectangular plate of glass, measured at rest, has sides \(30.0 \mathrm{cm}\) and \(60.0 \mathrm{cm} .\) (a) As measured in a reference frame moving parallel to the 60.0 -cm edge at speed \(0.25 c\) with respect to the glass, what are the lengths of the sides? (b) How fast would a reference frame have to move in the same direction so that the plate of glass viewed in that frame is square?
For a nonrelativistic particle of mass \(m,\) show that \(K=p^{2} /(2 m) .\) [Hint: Start with the nonrelativistic expressions for kinetic energy \(K\) and momentum \(p\).]
Two atomic clocks are synchronized. One is put aboard a spaceship that leaves Earth at \(t=0\) at a speed of \(0.750 c .\) (a) When the spaceship has been traveling for \(48.0 \mathrm{h}\) (according to the atomic clock on board), it sends a radio signal back to Earth. When would the signal be received on Earth, according to the atomic clock on Earth? (b) When the Earth clock says that the spaceship has been gone for \(48.0 \mathrm{h},\) it sends a radio signal to the spaceship. At what time (according to the spaceship's clock) does the spaceship receive the signal?
A spaceship travels toward Earth at a speed of \(0.97 c .\) The occupants of the ship are standing with their torsos parallel to the direction of travel. According to Earth observers, they are about \(0.50 \mathrm{m}\) tall and $0.50 \mathrm{m}$ wide. What are the occupants' (a) height and (b) width according to others on the spaceship?
An extremely relativistic particle is one whose kinetic energy is much larger than its rest energy. Show that for an extremely relativistic particle $E \approx p c$.
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