Why Are We Bombarded by Muons? Muons are unstable subatomic particles that decay to electrons with a mean lifetime of 2.2 μ s. They are produced when cosmic rays bombard the upper atmosphere about 10 km above the earth’s surface, and they travel very close to the speed of light . The problem we want to address is why we see any of them at the earth’s surface. (a) What is the greatest distance a muon could travel during its 2.2- μ s lifetime? (b) According to your answer in part (a), it would seem that muons could never make it to the ground. But the 2.2 μ S lifetime is measured in the frame of the muon, and muons are moving very fast. At a speed of 0.999c, what is the mean lifetime of a muon as measured by an observer at rest on the earth? How far would the muon travel in this time? Does this result explain why we find muons in cosmic rays? (c) From the point of view of the muon, it still lives for only 2.2 μ s. so how does it make it to the ground? What is the thickness of the 10 km of atmosphere through which the muon must travel, as measured by the muon? Is it now clear how the muon is able to reach the ground?
Why Are We Bombarded by Muons? Muons are unstable subatomic particles that decay to electrons with a mean lifetime of 2.2 μ s. They are produced when cosmic rays bombard the upper atmosphere about 10 km above the earth’s surface, and they travel very close to the speed of light . The problem we want to address is why we see any of them at the earth’s surface. (a) What is the greatest distance a muon could travel during its 2.2- μ s lifetime? (b) According to your answer in part (a), it would seem that muons could never make it to the ground. But the 2.2 μ S lifetime is measured in the frame of the muon, and muons are moving very fast. At a speed of 0.999c, what is the mean lifetime of a muon as measured by an observer at rest on the earth? How far would the muon travel in this time? Does this result explain why we find muons in cosmic rays? (c) From the point of view of the muon, it still lives for only 2.2 μ s. so how does it make it to the ground? What is the thickness of the 10 km of atmosphere through which the muon must travel, as measured by the muon? Is it now clear how the muon is able to reach the ground?
Why Are We Bombarded by Muons? Muons are unstable subatomic particles that decay to electrons with a mean lifetime of 2.2 μs. They are produced when cosmic rays bombard the upper atmosphere about 10 km above the earth’s surface, and they travel very close to the speed of light. The problem we want to address is why we see any of them at the earth’s surface. (a) What is the greatest distance a muon could travel during its 2.2-μs lifetime? (b) According to your answer in part (a), it would seem that muons could never make it to the ground. But the 2.2 μS lifetime is measured in the frame of the muon, and muons are moving very fast. At a speed of 0.999c, what is the mean lifetime of a muon as measured by an observer at rest on the earth? How far would the muon travel in this time? Does this result explain why we find muons in cosmic rays? (c) From the point of view of the muon, it still lives for only 2.2 μs. so how does it make it to the ground? What is the thickness of the 10 km of atmosphere through which the muon must travel, as measured by the muon? Is it now clear how the muon is able to reach the ground?
Definition Definition Rate at which light travels, measured in a vacuum. The speed of light is a universal physical constant used in many areas of physics, most commonly denoted by the letter c . The value of the speed of light c = 299,792,458 m/s, but for most of the calculations, the value of the speed of light is approximated as c = 3 x 10 8 m/s.
î
A proton is projected in the positive x direction into a region of uniform electric field E = (-5.50 x 105) i N/C at t = 0. The
proton travels 7.20 cm as it comes to rest.
(a) Determine the acceleration of the proton.
magnitude 5.27e13
direction -X
m/s²
(b) Determine the initial speed of the proton.
8.71e-6
magnitude The electric field is constant, so the force is constant, which means the acceleration will be constant.
m/s
direction +X
(c) Determine the time interval over which the proton comes to rest.
1.65e-7
Review you equations for constant accelerated motion. s
Three charged particles are at the corners of an equilateral triangle as shown in the figure below. (Let q = 2.00 μC, and
L = 0.750 m.)
y
7.00 με
60.0°
L
9
-4.00 μC
x
(a) Calculate the electric field at the position of charge q due to the 7.00-μC and -4.00-μC charges.
112
Once you calculate the magnitude of the field contribution from each charge you need to add these as vectors.
KN/CI + 64
×
Think carefully about the direction of the field due to the 7.00-μC charge. KN/Cĵ
(b) Use your answer to part (a) to determine the force on charge q.
240.0
If you know the electric field at a particular point, how do you find the force that acts on a charge at that point? mN
Î + 194.0
×
If you know the electric field at a particular point, how do you find the force that acts on a charge at that point? mN
In the Donkey Kong Country video games you often get around by shooting yourself out of barrel cannons. Donkey Kong wants to launch out of one barrel and land in a different one that is a distance in x of 9.28 m away. To do so he launches himself at a velocity of 22.6 m/s at an angle of 30.0°. At what height does the 2nd barrel need to be for Donkey Kong to land in it? (measure from the height of barrel 1, aka y0=0)
Chapter 37 Solutions
Mastering Physics with Pearson eText -- Standalone Access Card -- for University Physics with Modern Physics (14th Edition)
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