An electron with a total energy of 19GeV travels through an accelerator tube with proper length 7.7km. a) What is the length of the tube in the electron's frame? E= m b) How long does it take in the frame of the electron? E= s c) How long does it take in the frame of the tube? T= s Note: the rest energy of an electron is: 0=0.51MeV.

a) Approximately 0.2066 m

b) 0.00002568443 s

c) Approximately 188.87 s

Explanation:

a) The total energy of the electron = 190GeV

The rest energy of the electron = 0.51 MeV

u = √(299792458² × (1 - 1/37254.902²)) = 299792457.892

β = v/c = 299792457.892/299792458 = 0.99999999964

Δx = √(Δx'²×(1 - β²)) = √(7700²×(1 - 0.99999999964²)) ≈ 0.2066 m

The length of the tube in the electron's frame ≈ 0.2066 m

b) The time in the frame of the electron is given as follows;

Δt' = 7700/299792457.892 = 0.00002568443 s

c) The time in the frame of the tube is given as follows;

1 - β² = (Δt'/Δt)²

Δt = √(Δt'/(1 - β²)) = √(0.00002568443 /(1 - 0.99999999964²)) ≈ 188.87 s.

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air exerts forces on falling objects near earth’s surface.

explanation:

the term 'free falls' refer to object that are falling towards the earth, in a situation in which gravity is the only force acting on the object.

for an object in free fall, the acceleration is constant (g, the gravitational acceleration), and so the velocity of the object constantly increases.

for objects near earth's surface, there is always another force acting on the object: the resistance due to the air. this force is opposed to the direction of fall of the object, and it is proportional to the velocity of the object, so as the object falls down, this force increases up to a point when it balances the force of gravity, and the object continues its motion at constant velocity (called terminal velocity). since in this case gravity is not the only force acting on the object, we are not in a situation of free fall.