What are the big 5 equations for physics

How fast must an object move before its length appears to be contracted to one-fourth its proper length? (Give your answer in te

Tresset [83]

Answer:

0.97c

Explanation:

From the relativistic equation for length contraction, we have

$l$ = $l_{0}\sqrt{1 - \beta }$

where

$l$ is the final length of the object

$l_{0}$ is the original length of the object before contraction

β = $v^{2} /c^2$

where v is the speed of the object

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

The equation can be re-written as

$l$ / $l_{0}$ = $\sqrt{1 - \beta }$

For the length to contract to one-fourth of the proper length, then

$l$ / $l_{0}$ = 1/4

substituting into the equation, we'll have

1/4 = $\sqrt{1 - \beta }$

substituting for β, we'll have

1/4 = $\sqrt{1 - v^2/c^2 }$

squaring both side of the equation, we'll have

1/16 = 1 - $v^2/c^2$

$v^2/c^2$ = 1 - 1/16

$v^2/c^2$ = 15/16

square root both sides of the equation, we have

v/c = 0.968

v = 0.97c

3 0

3 years ago

A cave explorer travels 3.00 m eastward, then 6.50 m northward, and finally 12.0 m westward. Find the magnitude of the net displ

mina [271]

3 meters east and 15 meters west evens out to 12 meters west. the answer is 12 meters west

7 0

3 years ago

WGVU-AM is a radio station that serves the Grand Rapids, Michigan area. The main broadcast frequency is 1480kHz. At a certain di

Yuki888 [10]

Answer:

a

$\lambda = 202.7 \ m$

b

$w = 9.3 *10^{6} \ rad/s$

c

$k = 0.031 m^{-1}$

d

$E_{max} = 9.0 *10^{-3} \ V/m$

Explanation:

From the question we are told that

The frequency of the radio station is $f= 1480 \ kHz = 1480 *10^{3}\ Hz$

The magnitude of the magnetic field is $B = 3.0* 10^{-11} \ T$

Generally the wavelength is mathematically represented as

$\lambda = \frac{c}{f}$

Here c is the speed of light with value $c = 3.0 *10^{8} \ m/s$

So

$\lambda = \frac{3.0 *10^{8}}{ 1480 *10^{3}}$

=> $\lambda = 202.7 \ m$

Generally the angular frequency is mathematically represented as

$w = 2 \pi * f$

=> $w = 2 * 3.142 * 1480 *10^{3}$

=> $w = 9.3 *10^{6} \ rad/s$

Generally the wave number is mathematically represented as

=> $k = \frac{2 \pi }{\lambda}$

=> $k = \frac{2 * 3.142 }{ 202.7}$

=> $k = 0.031 m^{-1}$

Generally the amplitude of the electric field at this distance from the transmitter is mathematically represented as

$E_{max} = c * B$

=> $E_{max} = 3.0 *10^{8} * 3.0* 10^{-11}$

=> $E_{max} = 9.0 *10^{-3} \ V/m$

3 0

3 years ago

A child of mass 25 kg is skating fast, +10 m/s, and tries to get revenge by colliding with the 60 kg adult who is sitting still.

tankabanditka [31]

Answer: -4.4 m/s

Explanation:

This problem can be solved by the Conservation of Momentum principle, which establishes that the initial momentum $p_{o}$ must be equal to the final momentum $p_{f}$ :

$p_{o}=p_{f}$ (1)

Where:

$p_{o}=m_{1}V_{o}+m_{2}U_{o}$ (2)

$p_{f}=m_{1}V_{f}+m_{2}U_{f}$ (3)

$m_{1}=25 kg$ is the mass of the child

$V_{o}=10 m/s$ is the initial velocity of the child

$m_{2}=60 kg$ is the mass of the adult

$U_{o}=0 m/s$ is the initial velocity of the adult (it is sitting still)

$V_{f}$ is the final velocity of the child

$U_{f}=6 m/s$ is the final velocity of the adult

Substituting (2) and (3) in (1):

$m_{1}V_{o}+m_{2}U_{o}=m_{1}V_{f}+m_{2}U_{f}$ (4)

Isolating $V_{f}$ :

$V_{f}=\frac{m_{1}V_{o}-m_{2}U_{f}}{m_{1}}$ (5)

$V_{f}=\frac{(25 kg)(10 m/s)-(60 kg)(6 m/s)}{25 kg}$ (6)

Finally:

$V_{f}=-4.4 m/s$ This means the velocity of the child is in the opposite direction

4 0

3 years ago

help please. In 1961 the mlar atomic mass of carbon 12 was defined to be exactly 12g/mol (a value agreed upon by chemists and ph

Ne4ueva [31]

The first notion of the number of molecules per atom was calculated by Josef Loschmidt which he endeavored to complete in 1895. In his experiment, he determined the number of molecules in one cubic centimeter of gas under STP. this is equal to approx 2.6 x 10^19 molecules. The former is called "Loschmidt's Constant" instead.

4 0

3 years ago