"v0" means that there are no friction forces at that speed
<span>mgsinΘ = (mv0²/r)cosΘ → the variable m cancels </span>
<span>sinΘ/cosΘ = tanΘ = v0² / gr
</span><span>Θ = arctan(v0² / gr) </span>
<span>When v > v0, friction points downslope: </span>
<span>mgsinΘ + µ(mgcosΘ + (mv²/r)sinΘ) = (mv²/r)cosΘ → m cancels: </span>
<span>gsinΘ + µ(gcosΘ + (v²/r)sinΘ) = (v²/r)cosΘ </span>
<span>µ = ((v²/r)cosΘ - gsinΘ) / (gcosΘ + (v²/r)sinΘ) </span>
<span>where Θ is defined above. </span>
<span>When v > v0, friction points upslope: </span>
<span>mgsinΘ - µ(mgcosΘ + (mv²/r)sinΘ) = (mv²/r)cosΘ → m cancels: </span>
<span>gsinΘ - µ(gcosΘ + (v²/r)sinΘ) = (v²/r)cosΘ </span>
<span>µ = (gsinΘ - (v²/r)cosΘ) / (gcosΘ + (v²/r)sinΘ) </span>
<span>where Θ is defined above. </span>
distance to the star Betelgeuse: 640 ly
As we know that

also we know that


So the distance of Betelgeuse = 640 ly

distance to the star VY Canis Majoris: 


distance to the galaxy Large Magellanic Cloud: 49976 pc


now we have


distance to Neptune at the farthest: 4.7 billion km

now the order of distance from least to greatest is as following
1. distance to Neptune at the farthest
2. distance of Betelgeuse
3. distance to the star VY Canis Majoris
4. distance to the galaxy Large Magellanic Cloud
Answer:The electric field is zero and the potential is positive.
Explanation:
Two identical positive charges are separated by a certain distance and midway between charges two identical positive charges are placed near each other.
So the Electric field at midway is zero because the electric field due to both charges add up to give zero electric field.(because they point in opposite direction)
Potential is scalar quantity and charges are positive so they add up to give potential.
<h3><u>Answer;</u></h3>
D) Standing wave
<h3><u>Explanation;</u></h3>
- Standing wave also called stationary wave is a wave which oscillates in time but whose peak amplitude profile does not move in space.
- A standing wave pattern is a vibrational pattern created within a medium when the vibrational frequency of the source causes reflected waves from one end of the medium to interfere with incident waves from the source.
- Examples of standing waves include the vibration of a violin string and electron orbitals in an atom.
Answer:
Speed will be equal to 1.40 m/sec
Explanation:
Mass of the rubber ball m = 5.24 kg = 0.00524 kg
Spring is compressed by 5.01 cm
So x = 5.01 cm = 0.0501 m
Spring constant k = 8.08 N/m
Frictional force f = 0.031 N
Distance moved by ball d = 15.8 cm = 0.158 m
Energy gained by spring

Energy lost due to friction

So remained energy to move the ball = 0.0101 - 0.0048 = 0.0052 J
This energy will be kinetic energy


v = 1.40 m/sec