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:
15 N and 3.061
Explanation:
From the question,
The minimum force of friction to keep the book from sliding = 15 N.
using
F = mgμ................. Equation 1
Where F = Frictional Force, m = mass of the book, g = acceleration due to gravity, μ = coefficient of friction.
make μ the subject of the equation
μ = F/mg............... Equation 2
Given: F = 15 N, m = 0.5 kg, g = 9.8 m/s²
Substitute into equation 2
μ = 15(0.5×9.8)
μ = 15/4.9
μ = 3.061
Hence the coefficient of friction to keep the book from sliding = 3.061
To answer this question, we will refer to the attached diagram which represents the complete rock cycle.
Rock 1:Formed when rock 2 and rock 3 were subjected to intense heat and pressure inside the earth.
Referring to the diagram, we will find that heat and pressure are the factors required to form metamorphic rocks
Therefore, rock 1 is metamorphicRock 2:Formed when rock 1 and rock 3 were broken down into mineral (sediments) which accumulate and are subjected to pressure.
Referring to the diagram, we will find that this description would lead to the formation of sedimentary rocks.
Therefore, rock 2 is a sedimentary rock.Rock 3:Formed when rock 1 and rock 2 were buried inside the earth and melted because of heat and magma.
Referring to the diagram, we would find that melting then cooling of magma would lead to formation of igneous rock.
Therefore, rock 3 is igneous rock.Based on the above, the correct choice would be:Rock 1: Metamorphic
Rock 2: Sedimentary
Rock 3: Igneous
15 because i did the math, had this assignment, and also watch a video