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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 spaceship travels at constant velocity from Earth to a point 710 ly away as measured in Earth's rest frame. The ship's speed relative to Earth is $0.9999 c .$ A passenger is 20 yr old when departing from Earth. (a) How old is the passenger when the ship reaches its destination, as measured by the ship's clock? (b) If the spaceship sends a radio signal back to Earth as soon as it reaches its destination, in what year, by Earth's calendar, does the signal reach Earth? The spaceship left Earth in the year 2000.
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 $E \approx p c$.

At the 10.0 -km-long Stanford Linear Accelerator, electrons with rest energy of 0.511 MeV have been accelerated to a total energy of \(46 \mathrm{GeV}\). How long is the accelerator as measured in the reference frame of the electrons?
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?
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