Ask question

Ask question

All categories

2 years ago

6

A rod of propoer length l0 is at rest in frame S'. it ilies in the x',y' plane and amkes an angle of sin^-1(3/5) What must be th

e value of v if as measured in S the rod is at a 45 degree)

1 answer:

Blizzard [7]2 years ago

5 0

Answer:

v = 1.98*10^8 m/s

Explanation:

Given:

- Rod at rest in S' frame

- makes an angle Q = sin^-1 (3/5) in reference frame S'

- makes an angle of 45 degree in frame S

Find:

What must be the value of v if as measured in S the rod is at a 45 degree)

Solution:

- In reference frame S'

x' component = L*cos(Q)

y' component = L*sin(Q)

- Apply length contraction to convert projected S' frame lengths to S frame:

x component = L*cos(Q) / γ (Length contraction)

y component = L*sin(Q) (No motion)

- If the rod is at angle 45° to the x axis, as measured in F, then the x and y components must be equal:

L*sin(Q) = L*cos(Q) / γ

Given: γ = c / sqrt(c^2 - v^2)

c / sqrt(c^2 - v^2) = cot(Q)

1 - (v/c)^2 = tan(Q)

v = c*sqrt( 1 - tan^2 (Q))

For the case when Q = sin^-1 (3/5)::

tan(Q) = 3/4

v = c*sqrt( 1 - (3/4)^2)

v = c*sqrt(7) / 4 = 1.98*10^8 m/s

You might be interested in

During a trial run, race car A starts from rest and accelerates uniformly along a straight level track for a particular interval

kondor19780726 [428]

Answer: car B has travelled 4times as far as Car A

d=vi*t+1/2at^2

No initial velocity so equation becomes;

d=1/2at^2 and the acceleration is the same between both only time is different;

Car A d=1/2a(1)^2

Car B d=1/2a(2)^2

Car A d= 1^2=1

Car B d= 2^2=4

Car B d=4*Car A

So car B has travelled 4 times as far as car A

5 0

2 years ago

Use this free body diagram to help you find the magnitude of the force F1 needed to keep this block in static equilibrium 15.3 N

bija089 [108]

Do you have a picture of the diagram?

5 0

3 years ago

A spring stretches 0.150 m when a 0.30 kg mass is hung from it. The spring is then stretched an additional 0.100 m from this equ

DochEvi [55]

Answer:

a) $k=19.6N/m$

b) $V_m=0.81m/s$

c) $a_m=6.561m/s^2$

d) $K.E=0.096J$

e) $T=0.78sec$ & $F=1.29sec$

f) $mx'' + kx' =0$

Explanation:

From the question we are told that:

Stretch Length $L=0.150m$

Mass $m=0.30kg$

Total stretch length $L_t=0.150+0.100=>0.25$

a)

Generally the equation for Force F on the spring is mathematically given by

$F=-km\\\\k=F/m\\\\k=\frac{m*g}{x}\\\\k=\frac{0.30*9.8}{0.15}$

$k=19.6N/m$

b)Generally the equation for Max Velocity of Mass on the spring is mathematically given by

$V_m=A\omega$

Where

A=Amplitude

$A=0.100m$

And

$\omega=angulat Velocity\\\\\omega=\sqrt{\frac{k}{m}}\\\\\omega=\sqrt{\frac{19.6}{0.3}}\\\\\omega=8.1rad/s$

Therefore

$V_m=A\omega\\\\V_m=8.1*0.1$

$V_m=0.81m/s$

c)

Generally the equation for Max Acceleration of Mass on the spring is mathematically given by

$a_m=\omega^2A$

$a_m=8.1^2*0.1$

$a_m=6.561m/s^2$

d)

Generally the equation for Total mechanical energy of Mass on the spring is mathematically given by

$K.E=\frac{1}{2}mv^2$

$K.E=\frac{1}{2}*0.3*0.8^2$

$K.E=0.096J$

e)

Generally the equation for the period T is mathematically given by

$\omega=\frac{2\pi}{T}$

$T=\frac{2*3.142}{8.1}$

$T=0.78sec$

Generally the equation for the Frequency is mathematically given by

$F=\frac{1}{T}$

$F=1.29sec$

f)

Generally the Equation of time-dependent vertical position of the mass is mathematically given by

$mx'' + kx' =0$

Where

'= signify order of differentiation

7 0

3 years ago

A sinusoidal wave is traveling along a rope. The oscillator that generates the wave completes 40.0 vibrations in 30.0s . A given

Phantasy [73]

From the solution that I have done, the wavelength in the question that we have is 31.88 cm

<h3>How to solve for the wavelength</h3>

The frequency in the question is given as 40/30 = 1.33 hz

Next we have to solve for V

= 425/10

= 42.5 cm/s

v = frequency * wavelength

we have to put in the values in the formula. This would be

42.5 = 1.33 x wavelength

we have to divide through by 1.33 to get the wavelength. This would be

42.5/1.333 = wavelength

31.88 cm = wavelength

Hence we can say that the wavelength in the question that we have here is 31.88 cm

Read more on wavelength here:

brainly.com/question/10728818

#SPJ4

8 0

1 year ago

What is escape velocity

DanielleElmas [232]

Escape velocity is the speed that an object needs to be traveling to break free of a planet or moon's gravity well and leave it without further propulsion. For example, a spacecraft leaving the surface of Earth needs to be going 7 miles per second, or nearly 25,000 miles per hour to leave without falling back to the surface or falling into orbit.

8 0

2 years ago