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]
Carbon atoms and hydrogen I hope this helps
Hi there!
We know that:
U (Potential energy) = mgh
We are given the potential energy, so we can rearrange to solve for h (height):
U/mg = h
g = 9.81 m/s²
m = 30 g ⇒ 0.03 kg
0.062/(0.03 · 9.81) = 0.211 m
Answer:
True
Explanation:
If we swing a bucket of water fast enough in a vertical circle the water does not spill out even at the top-most position of the bucket. This happens because the centrifugal force acting away from the center in a circular motion neutralizes or overcomes the gravitational force on the water particles.
<u>Centrifugal force is mathematically related as:</u>
where:
m = mass of the revolving body
r = radius of revolution
angular velocity in radians per second
This force F acts in radially outward direction.
