Answer:
F = GMmx/[√(a² + x²)]³
Explanation:
The force dF on the mass element dm of the ring due to the sphere of mass, m at a distance L from the mass element is
dF = GmdM/L²
Since the ring is symmetrical, the vertical components of this force cancel out leaving the horizontal components to add.
So, the horizontal components add from two symmetrically opposite mass elements dM,
Thus, the horizontal component of the force is
dF' = dFcosФ where Ф is the angle between L and the x axis
dF' = GmdMcosФ/L²
L² = a² + x² where a = radius of ring and x = distance of axis of ring from sphere.
L = √(a² + x²)
cosФ = x/L
dF' = GmdMcosФ/L²
dF' = GmdMx/L³
dF' = GmdMx/[√(a² + x²)]³
Integrating both sides we have
∫dF' = ∫GmdMx/[√(a² + x²)]³
∫dF' = Gm∫dMx/[√(a² + x²)]³ ∫dM = M
F = GmMx/[√(a² + x²)]³
F = GMmx/[√(a² + x²)]³
So, the force due to the sphere of mass m is
F = GMmx/[√(a² + x²)]³
The answer to the question
Answer:
A plant cell contains a large, singular vacuole that is used for storage and maintaining the shape of the cell. In contrast, animal cells have many, smaller vacuoles. Plant cells have a cell wall, as well as a cell membrane. Animal cells simply have a cell membrane, but no cell wall.
hope this helps :)
Answer:
2.5 kg.m/s
Explanation:
Taking left side as positive while right side direction as negative then
Momentum, p= mv where m is the mass of the object and v is the velocity of travel
Momentum for ball moving towards right side=mv=2.5*-3=-7.5 kg.m/s
Momentum for the ball moving towards the left side=mv=2.5*4=10 kg.m/s
Total momentum=-7.5 kg.m/s+10 kg.m/s=2.5 kg.m/s
Answer:
22.2 W
Explanation:
First of all, we calculate the work done by moving the wagon, using the formula:
where
F = 20 N is the magnitude of the force
d = 1000 m is the displacement of the wagon
is the angle between the direction of the force and of the displacement (assuming the force is applied in the direction of motion)
Substituting, we find
Now we can find the power generated, which is equal to the ratio between the work done and the time taken:
where
W = 20,000 J
t = 15 min = 900 s
Substituting,
And the same value in Joules/second (remember that 1 Watt = 1 Joule/second)
