Explanation:
Given that,
Weight of the friend, W = 600 N
When the friend sits on the metal frame it bends downward 4 cm, we can say that the compression in the it is 4 cm or 0.04 m
To find,
Spring constant for this chair or k
Solve :
The weight of an object is equal to the force exerted by the gravitational force, F = 600 N
According to Hooke's law, the force exerted by the spring is given by :
F = kx
k is the spring constant
k = 15000 N/m
Therefore, the spring constant of the spring is 15000 N/m.
Answer:
The shearing stress is 10208.3333 Pa
The shearing strain is 0.25
The shear modulus is 40833.3332 Pa
Explanation:
Given:
Block of gelatin of 120 mm x 120 mm by 40 mm
F = force = 49 N
Displacement = 10 mm
Questions: Find the shear modulus, Sm = ?, shearing stress, Ss = ?, shearing strain, SS = ?
The shearing stress is defined as the force applied to the block over the projected area, first, it is necessary to calculate the area:
A = 40*120 = 4800 mm² = 0.0048 m²
The shearing stress:
The shearing strain is defined as the tangent of the displacement that the block over its length:
Finally, the shear modulus is the division of the shearing stress over the shearing strain:
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
(a) 
According to Newton's second law, the force experienced by each balloon is given by:
F = ma
where
m = 0.021 kg is the mass
a = 1.1 m/s^2 is the acceleration
Substituting, we found:
The electrostatic force between the two balloons can be also written as
where
k is the Coulomb's constant
Q is the charge on each balloon
r = 16 m is their separation
Since we know the value of F, we can find Q, the magnitude of the charge on each balloon:
(b) 
electrons
The magnitude of the charge of one electron is
While the magnitude of the charge on one balloon is
This charge can be written as
where N is the number of electrons that are responsible for this charge. Solving for N, we find:
One way that the world's ocean affects weather and climate is by playing an important role in keeping our planet warm. ... The ocean doesn't just store solar radiation; it also helps to distribute heat around the globe. When water molecules are heated, they exchange freely with the air in a process called evaporation.
