Given:
k = 100 lb/ft, m = 1 lb / (32.2 ft/s) = 0.03106 slugs
Solution:
F = -kx
mx" = -kx
x" + (k/m)x = 0
characteristic equation:
r^2 + k/m = 0
r = i*sqrt(k/m)
x = Asin(sqrt(k/m)t) + Bcos(sqrt(k/m)t)
ω = sqrt(k/m)
2π/T = sqrt(k/m)
T = 2π*sqrt(m/k)
T = 2π*sqrt(0.03106 slugs / 100 lb/ft)
T = 0.1107 s (period)
x(0) = 1/12 ft = 0.08333 ft
x'(0) = 0
1/12 = Asin(0) + Bcos(0)
B = 1/12 = 0.08333 ft
x' = Aω*cos(ωt) - Bω*sin(ωt)
0 = Aω*cos(0) - (1/12)ω*sin(0)
0 = Aω
A = 0
So B would be the amplitude. Therefore, the equation of motion would be x
= 0.08333*cos[(2π/0.1107)t]
Answer: 24.1 mL
Explanation:
Initial volume V1 = 65 mL
Initial pressure P1 = 0.854 atm
Final volume of the gas V2 = ?
Final pressure of the gas P2 = 2.3 atm
Since, pressure and volume are involved while temperature is constant, apply the formula for Boyle's law
P1V1 = P2V2
0.854 atm x 65 mL = 2.3 atm x V2
55.51 atm mL = 2.3 atm x V2
V2 = (55.51 atm mL / 2.3 atm)
V2 = 24.1 mL
Thus, the final volume of the gas will be
24.1 mL
Answer:
Plate separation of each capacitor is 101.132 °A
Explanation:
The formula to calculate the capacitance in empty space as a function of distance (square parallel plates) is:
clearing for distance:
The magnitude of the net force that is acting on particle q₃ is equal to 6.2 Newton.
<u>Given the following data:</u>
Charge = C.
Distance = 0.100 m.
<u>Scientific data:</u>
Coulomb's constant =
<h3>How to calculate the net force.</h3>
In this scenario, the magnitude of the net force that is acting on particle q₃ is given by:
F₃ = F₁₃ + F₂₃
Mathematically, the electrostatic force between two (2) charges is given by this formula:
<u>Where:</u>
- r is the distance between two charges.
<u>Note:</u> d₁₃ = 2d₂₃ = 2(0.100) = 0.200 meter.
For electrostatic force (F₁₃);
F₁₃ = 1.24 Newton.
For electrostatic force (F₂₃);
F₂₃ = 4.96 Newton.
Therefore, the magnitude of the net force that is acting on particle q₃ is given by:
F₃ = 1.24 + 4.96
F₃ = 6.2 Newton.
Read more on charges here: brainly.com/question/14372859
Explanation:
c. if the vector is oriented at 0° from the X -axis.