Answer:
0.191 s
Explanation:
The distance from the center of the cube to the upper corner is r = d/√2.
When the cube is rotated an angle θ, the spring is stretched a distance of r sin θ. The new vertical distance from the center to the corner is r cos θ.
Sum of the torques:
∑τ = Iα
Fr cos θ = Iα
(k r sin θ) r cos θ = Iα
kr² sin θ cos θ = Iα
k (d²/2) sin θ cos θ = Iα
For a cube rotating about its center, I = ⅙ md².
k (d²/2) sin θ cos θ = ⅙ md² α
3k sin θ cos θ = mα
3/2 k sin(2θ) = mα
For small values of θ, sin θ ≈ θ.
3/2 k (2θ) = mα
α = (3k/m) θ
d²θ/dt² = (3k/m) θ
For this differential equation, the coefficient is the square of the angular frequency, ω².
ω² = 3k/m
ω = √(3k/m)
The period is:
T = 2π / ω
T = 2π √(m/(3k))
Given m = 2.50 kg and k = 900 N/m:
T = 2π √(2.50 kg / (3 × 900 N/m))
T = 0.191 s
The period is 0.191 seconds.
The amount of gold in decigrams if 450 micrograms is needed is 4.5 × 10-³ decigrams.
<h3>How to convert micrograms to decigrams?</h3>
According to this question, 450 micrograms of a sample of gold is needed but we only have a mass balance that measures in decigrams.
This means that we are to convert the amount of gold you need to decigrams by comparing the exponents.
The conversion factor of micrograms to decigrams is as follows:
1 micrograms = 1 × 10-⁵ decigrams
This means 450 micrograms is equivalent to 450 × 1 × 10-⁵ = 4.5 × 10-³ decigrams
Therefore, the amount of gold in decigrams if 450 micrograms is needed is 4.5 × 10-³ decigrams.
Learn more about decigrams at: brainly.com/question/6869599
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Answer:
negative ion
Explanation:
An atom that has fewer neutrons than protons and more electrons than protons is a negative ion.
The positively charged particles in an atom are the protons
The negatively charged particles in an atom are the electrons.
The charge an atom carries depends on the balance between the number of protons and electrons in an atom.
- When the number of protons is more than the number of electrons, the atom is positively charged.
- When the number of electrons is more than the number of protons, the atom is negatively charged.
Explanation:
Write in scientific notation.
4000 = 4.0×10³
Answer:
= 6 cm/s
Explanation:
<u><em>Given:</em></u>
Acceleration = a = 2 cm/s²
Time = t = 3s
Initial Velocity = 
= 0 cm/s
<u><em>Required:</em></u>
Velocity = = ?
<u><em>Formula:</em></u>
a = 
<u><em>Solution:</em></u>
2 = 
=> = 2*3
=> = 6 cm/s
