A) The answer is 11.53 m/s
The final kinetic energy (KEf) is the sum of initial kinetic energy (KEi) and initial potential energy (PEi).
KEf = KEi + PEi
Kinetic energy depends on mass (m) and velocity (v)
KEf = 1/2 m * vf²
KEi = 1/2 m * vi²
Potential energy depends on mass (m), acceleration (a), and height (h):
PEi = m * a * h
So:
KEf = KEi + <span>PEi
</span>1/2 m * vf² = 1/2 m * vi² + m * a * h
..
Divide all sides by m:
1/2 vf² = 1/2 vi² + a * h
We know:
vi = 9.87 m/s
a = 9.8 m/s²
h = 1.81 m
1/2 vf² = 1/2 * 9.87² + 9.8 * 1.81
1/2 vf² = 48.71 + 17.74
1/2 vf² = 66.45
vf² = 66.45 * 2
vf² = 132.9
vf = √132.9
vf = 11.53 m/s
b) The answer is 6.78 m
The kinetic energy at the bottom (KE) is equal to the potential energy at the highest point (PE)
KE = PE
Kinetic energy depends on mass (m) and velocity (v)
KE = 1/2 m * v²
Potential energy depends on mass (m), acceleration (a), and height (h):
PE = m * a * h
KE = PE
1/2 m * v² = m * a * h
Divide both sides by m:
1/2 * v² = a * h
v = 11.53 m/s
a = 9.8 m/s²
h = ?
1/2 * 11.53² = 9.8 * h
1/2 * 132.94 = 9.8 * h
66.47 = 9.8 * h
h = 66.47 / 9.8
h = 6.78 m
Answer:
minimum thickness of the coating = 122.868 nm
Explanation:
Given data
lens index of refraction = 1.29
wavelength = 634 nm
glass index of refraction = 1.53
to find out
minimum thickness of the coating
solution
we have given non reflective coating
so
we know that minimum thickness of the coating formula
minimum thickness of the coating = Wavelength / 4n
here n is coating index of refraction
so put here both value to get thickness
minimum thickness of the coating = Wavelength / 4n
minimum thickness of the coating = 634 / 4 ( 1.29 )
so minimum thickness of the coating = 122.868 nm
Answer:
4.7m
Explanation:
Given parameters:
Mass of the book = 1kg
Gravitational potential energy = 46J
Unknown:
Height of the shelf = ?
Solution:
The potential energy is due to the position of a body above the ground.
Gravitational potential energy = mgh
m is the mass,
g is the acceleration due gravity = 9.8m/s²
h is the height which is unknown
46 = 1 x 9.8 x h
h = 4.7m
Answer:
C. 5.6 × 10^11 N/C
Explanation:
The electric field
at a distance
from a charge
is given by

where
is the coulomb's constant.
Now, in our case

;
therefore,


which is choice C from the options given<em> (at least it resembles it).</em>
Answer:
Part a)

Part b)
if both sides are rough then it will reach the same height on the other side because the energy is being conserved.
Part c)
Since marble will go to same height when it is rough while when it is smooth then it will go to the height

so on smooth it will go to lower height
Explanation:
As we know by energy conservation the total energy at the bottom of the bowl is given as

here we know that on the left side the ball is rolling due to which it is having rotational and transnational both kinetic energy
now on the right side of the bowl there is no friction
so its rotational kinetic energy will not change and remains the same
so it will have

now we know that


so we have




so the height on the smooth side is given as

Part b)
if both sides are rough then it will reach the same height on the other side because the energy is being conserved.
Part c)
Since marble will go to same height when it is rough while when it is smooth then it will go to the height

so on smooth it will go to lower height