Answer:
Explanation:
Given
mass of cylinder is M
radius R
velocity of center of mass is v
As there is no slipping therefore cylinder will rotate as well as translate
Moment of inertia of cylinder 
Kinetic Energy of cylinder 
Rotational energy 
for rolling
where 
Total kinetic Energy 
Energy transformation, also termed as energy conversion, is the process of changing energy from one of its forms into another. In physics, energy is a quantity that provides the capacity to perform many works—think of lifting or warming an object. In addition to being convertible, energy is transferable to a different location or object, but it cannot be created or destroyed.
Energy in many of its forms may be used in natural processes, or to provide some service to society such as heating, refrigeration, lighting or performing mechanical work to operate machines. For example, in order to heat your home, your furnace can burn fuel, whose chemical potential energy is thus converted into thermal energy, which is then transferred to your home's air in order to raise its temperature.
In another example, an internal combustion engine burns gasoline to create pressure that pushes the pistons, thus performing work in order to accelerate your vehicle, ultimately converting the fuel's chemical energy to your vehicle's additional kinetic energy corresponding to its increase in speed.
Contents
1 Entropy and limitations in conversion of thermal energy to other types
2 Transformation of kinetic energy of charged particles to electric energy
3 History of energy transformation from the early universe
4 Examples
4.1 Examples of sets of energy conversions in machines
4.2 Other energy conversions
5 See also
6 References
Answer:
3.64×10⁸ m
3.34×10⁻³ m/s²
Explanation:
Let's define some variables:
M₁ = mass of the Earth
r₁ = r = distance from the Earth's center
M₂ = mass of the moon
r₂ = d − r = distance from the moon's center
d = distance between the Earth and the moon
When the gravitational fields become equal:
GM₁m / r₁² = GM₂m / r₂²
M₁ / r₁² = M₂ / r₂²
M₁ / r² = M₂ / (d − r)²
M₁ / r² = M₂ / (d² − 2dr + r²)
M₁ (d² − 2dr + r²) = M₂ r²
M₁d² − 2dM₁ r + M₁ r² = M₂ r²
M₁d² − 2dM₁ r + (M₁ − M₂) r² = 0
d² − 2d r + (1 − M₂/M₁) r² = 0
Solving with quadratic formula:
r = [ 2d ± √(4d² − 4 (1 − M₂/M₁) d²) ] / 2 (1 − M₂/M₁)
r = [ 2d ± 2d√(1 − (1 − M₂/M₁)) ] / 2 (1 − M₂/M₁)
r = [ 2d ± 2d√(1 − 1 + M₂/M₁) ] / 2 (1 − M₂/M₁)
r = [ 2d ± 2d√(M₂/M₁) ] / 2 (1 − M₂/M₁)
When we plug in the values, we get:
r = 3.64×10⁸ m
If the moon wasn't there, the acceleration due to Earth's gravity would be:
g = GM / r²
g = (6.672×10⁻¹¹ N m²/kg²) (5.98×10²⁴ kg) / (3.64×10⁸ m)²
g = 3.34×10⁻³ m/s²
