Out of the choices given, when a light wave moves from a medium where particles of matter are closely packed to a medium made of little matter. You expect the light wave to move faster and increase its speed.
Answer:
The diameter of the axle is 5.08 cm.
Explanation:
Given that,
Force = 800 N
Distance = 78.0 m
Suppose we need to find the diameter of the axle be in order to raise the buckets at a steady 2.00 cm/s when it is turning at 7.5 rpm.
We need to calculate the radius of axle
Using formula of linear velocity
![v = r\omega](https://tex.z-dn.net/?f=v%20%3D%20r%5Comega)
![r=\dfrac{v}{\omega}](https://tex.z-dn.net/?f=r%3D%5Cdfrac%7Bv%7D%7B%5Comega%7D)
Where, v =velocity
r = radius
=angular velocity
Put the value into the formula
![r=\dfrac{2.00}{7.5\times\dfrac{2\pi}{60}}](https://tex.z-dn.net/?f=r%3D%5Cdfrac%7B2.00%7D%7B7.5%5Ctimes%5Cdfrac%7B2%5Cpi%7D%7B60%7D%7D)
![r=2.54\ cm](https://tex.z-dn.net/?f=r%3D2.54%5C%20cm)
We need to calculate the diameter of axle
Using formula of diameter
![d=2r](https://tex.z-dn.net/?f=d%3D2r)
![d=2\times2.54](https://tex.z-dn.net/?f=d%3D2%5Ctimes2.54)
![d=5.08\ cm](https://tex.z-dn.net/?f=d%3D5.08%5C%20cm)
Hence, The diameter of the axle is 5.08 cm.
To calculate the final velocity, we use Newton's first equation of linear motion:v=u+at
Where v is final velocity
u is initial velocity
a is the average acceleration
t is the time taken during acceleration.
Therefore,
v=0+2.5m/s²*6.00s
=15m/s
Decelerating from 15m/s;
v=15m/s+(-2m/s²×4.0s)
=3m/s
To get the distance it travelled, we use
v²=u²+2as
During acceleration, the distance travelled is calculated as below.
15²=0+2×2.5S
225=5S
S=45meters
During decellaration, displacement is calculated as below,
3²=15²+(2×4S)
9=225+8S
8S=216
S=27meters
Total displacement=45m+27m
=72 meters.