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3 years ago

The momentum of an electron is 1.75 times larger than the value computed non-relativistically. What is the speed of the electron

Physics

1 answer:

FrozenT [24]3 years ago

6 0

Answer:

Speed of the electron is 2.46 x 10^8 m/s

Explanation:

momentum of the electron before relativistic effect = $M_{0} V$

where $M_{0}$ is the rest mass of the electron

V is the velocity of the electron.

under relativistic effect, the mass increases.

under relativistic effect, the new mass M will be

M = $M_{0}/ \sqrt{1 - \beta ^{2} }$

where

$\beta = V/c$

c is the speed of light = 3 x 10^8 m/s

V is the speed with which the electron travels.

The new momentum will therefore be

==> $M_{0}V/ \sqrt{1 - \beta ^{2} }$

It is stated that the relativistic momentum is 1.75 times the non-relativistic momentum. Equating, we have

1.75 $M_{0} V$ = $M_{0}V/ \sqrt{1 - \beta ^{2} }$

the equation reduces to

1.75 = $1/ \sqrt{1 - \beta ^{2} }$

square both sides of the equation, we have

3.0625 = 1/ $(1 - \beta ^{2} )$

3.0625 - 3.0625 $\beta ^{2}$ = 1

2.0625 = 3.0625 $\beta ^{2}$

$\beta ^{2}$ = 0.67

β = 0.819

substitute for $\beta = V/c$

V/c = 0.819

V = c x 0.819

V = 3 x 10^8 x 0.819 = 2.46 x 10^8 m/s

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What steps are involved in converting potential energy to kinetic energy, or kinetic energy to potential energy?

Ray Of Light [21]

Explanation:

Potential energy is the energy obtained by an object due to the position of an object. Whereas kinetic energy is the energy obtained by an object due to its motion.

For example, an ball is placed over a building of height h. Then steps followed to covert its potential energy into kinetic energy are as follows.

Step 1: When ball is at placed over a building of height h, then it has only potential energy and no kinetic energy.

Step 2: A man pushes the ball and it moves in the downward direction.

Step 3: When ball starts to move or fall it gains kinetic energy, that is potential energy now becomes equal to 0.

Similarly, on reaching the ground and after bouncing a few times when it stop moving then kinetic energy converts into potential energy.

7 0

3 years ago

A laser beam enters a 12.0 cm thick glass window at an angle of 33.0° from the normal. The index of refraction of the glass is 1

Alenkinab [10]

Answer:

The time is 0.563 ns.

Explanation:

Given that,

Index of refraction of glass = 1.41

Distance = 12.0 cm

Angle = 33.0°

We need to calculate the refraction angle

Using Snell's law

$n_{1}\sin\theta=n_{r}\sin\theta$

put the value into the formula

$1\times\sin33=1.41\sin\theta$

$\sin\theta=\dfrac{1\times\sin33}{1.41}$

$\theta=22.71^{\circ}$

We need to calculate the velocity of beam in glass

Using formula of velocity

$v=\dfrac{c}{n}$

Put the value into the formula

$v=\dfrac{3\times10^{8}}{1.41}$

$v=2.13\times10^{8}\ m/s$

We need to calculate the time

Using formula of distance

$v=\dfrac{d}{t}$

$t=\dfrac{12.0\times10^{-2}}{2.13\times10^{8}}$

$t=5.63\times10^{-10}\ sec$

$t=0.563\times10^{-9}\ sec$

$t=0.563\ ns$

Hence, The time is 0.563 ns.

6 0

3 years ago

An object of mass 700700 kg is released from rest 20002000 m above the ground and allowed to fall under the influence of gravity

qwelly [4]

Answer:

59.503987 seconds

Explanation:

b = Proportionality constant = 50 Ns/m

g = Acceleration due to gravity = 9.81 m/s²

m = Mass of object = 700 kg

We have the equation of velocity

$v(t)=\dfrac{mg}{b}+\left(V_0-\dfrac{mg}{b}\right)e^{\dfrac{bt}{m}}$

The equation of motion

$x(t)=\dfrac{mg}{b}+\dfrac{m}{b}\left(V_0-\dfrac{mg}{b}\right)(1-e^{\dfrac{bt}{m}})$

$x(t)=\dfrac{700\times 9.81}{50}+\dfrac{9.81}{50}\left(0-\dfrac{700\times 9.81}{50}\right)(1-e^{\dfrac{50t}{700}})$

when x(t)=2000

$2000=\dfrac{700\times 9.81}{50}+\dfrac{9.81}{50}\left(0-\dfrac{700\times 9.81}{50}\right)(1-e^{\dfrac{50t}{700}})\\\Rightarrow 2000\times \:50=\frac{700\times \:9.81}{50}\times \:50+\frac{9.81}{50}\left(0-\frac{700\times \:9.81}{50}\right)\left(1-e^{\frac{50t}{700}}\right)\times \:50\\\Rightarrow 6867-\frac{67365.27}{50}\left(1-e^{\frac{50t}{700}}\right)=100000\\\Rightarrow 50\left(-\frac{67365.27}{50}\left(1-e^{\frac{50t}{700}}\right)\right)=93133\times \:50\\\Rightarrow \frac{-67365.27\left(1-e^{\frac{50t}{700}}\right)}{-67365.27}=\frac{4656650}{-67365.27}\\\Rightarrow 1-e^{\frac{50t}{700}}=-69.12538\dots\\\Rightarrow -e^{\frac{50t}{700}}=-70.12538\dots\\\Rightarrow t=14\ln \left(70.12538\dots \right)\\\Rightarrow t=59.50398\ s$

The time taken is 59.503987 seconds

8 0

2 years ago

The speed of light is about 3.00 × 105 km/s. It takes approximately 1.28 seconds for light reflected from the

Ulleksa [173]

Just to correct you - the speed of light is 3.0 x 10^5 km/sec and not 105 km/sec as given by you (maybe it was just a typing mistake from your end).

The average distance between earth and moon would be - 384,000 kms.

This is calculated by the formula -> Distance = Speed x Time.

8 0

3 years ago

Consider a point on a bicycle wheel as the wheel turns about a fixed axis, neither speeding up nor slowing down. Compare the lin

Natalija [7]

Answer:

c. Only the linear acceleration is zero.

Explanation:

The linear acceleration is defined as the rate of change of linear velocity. Since the bicycle is moving in the same direction, with the same speed, without speeding up or slowing down. Therefore, there will be no change in linear velocity and as a result, linear acceleration will be zero.

The angular acceleration is the rate of change of angular velocity. Since the angular velocity is changing its direction constantly. Therefore, it has a certain component of acceleration at all times called centripetal acceleration.

Therefore, the correct option is:

c. Only the linear acceleration is zero.

4 0

2 years ago