A) 1.55
The speed of light in a medium is given by:
where
is the speed of light in a vacuum
n is the refractive index of the material
In this problem, the speed of light in quartz is
So we can re-arrange the previous formula to find n, the index of refraction of quartz:
B) 550.3 nm
The relationship between the wavelength of the light in air and in quartz is
where
is the wavelenght in quartz
is the wavelength in air
n is the refractive index
For the light in this problem, we have
Therefore, we can re-arrange the equation to find , the wavelength in air:
Explanation:
The given data is as follows.
Angular velocity (
) = 2.23 rps
Distance from the center (R) = 0.379 m
First, we will convert revolutions per second into radian per second as follows.
= 2.23 revolutions per second
= 
= 14.01 rad/s
Now, tangential speed will be calculated as follows.
Tangential speed, v = 
= 0.379 x 14.01
= 5.31 m/s
Thus, we can conclude that the tack's tangential speed is 5.31 m/s.
By definition, the density of an object is given by:
Where,
M: mass of the object
V: volume of the object
Since the mass and volume of an object are numerical values greater than zero, then it follows that:
It is important to respect the units of each measure.
For this case we can use the grams for the mass and cubic centimeters for the volume.
Answer:
A possible value for density is given by:
Jane's mechanical energy at any time is
where
is the potential energy, while
is the kinetic energy.
Initially, Jane is on the ground, so the altitude is h=0 and the potential energy is zero: U=0. She's running with speed v, so she has kinetic energy only:
Then she grabs the vine, and when she reaches the maximum height h, her speed is zero: v=0, and so the kinetic energy becomes zero: K=0. So now her mechanical energy is just potential energy:
But E must be conserved, so the initial kinetic energy must be equal to the final potential energy:
from which we can find h, the maximum height Jane can reach:
