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:
1800J
Explanation:
Step one:
given data
mass of bullet m= 3g= 0.03kg
initial velocity u = 400m/s
final velocity v= 200 m/s
Step two:
1.The bullet's lost kinetic energy went inside the tree.
2. The energy transferred is computed as
= initial KE- KE final
Initial KE= 1/2mu^2
Initial KE= 1/2*0.03*400^2
Initial KE= 1/2*0.03*160000
Initial KE= 1/2*4800
Initial KE= 2400J
KE final= 1/2mv^2
KE final= 1/2*0.03*200^2
KE final= 1/2*0.03*40000
KE final= 1/2*1200
KE final= 600J
KE transferred = 2400-600
KE transferred= 1800J
R = 18 ohms
Explanation:
Given:
V = 36 volts
I = 2.0 A
R = ?
Use Ohm's law to solve for the resistance:
V = IR
or
R = V/I
= (36 volts)/(2.0 A)
= 18 ohms
Large bodies of water<span> such as oceans, seas, and large lakes </span>affect<span> the </span>climate<span> of an area. </span>Water<span> heats and cools more slowly than land. Thus, in the summer, the </span>coastal<span> regions </span>will<span> stay cooler and in winter warmer. A more moderate </span>climate<span> with a smaller temperature range </span>is<span> created.</span>
Answer:
Neutralization reactions always produce water and a salt.
Explanation:
There are different types of chemical reactions that occurs. Two of them are neutralization and double-displacement reaction. Neutralization reaction is the reaction between an acid and a base to give an acid salt and water as products. For example:
2NaOH (base) + H2SO4 (acid) → Na2SO4 (salt) + 2H2O (water)
On the other hand, Double displacement reaction is the reaction that involves an ion exchange between the reactants to form new products. This ionic exchange occurs in such a way that two reactants form two new products. For example:
2NaCl + Ca(NO3)2 → CaCl2 + 2NaNO3
Therefore, the major difference between these two types of reactions is that: NEUTRALIZATION MUST ALWAYS PRODUCE WATER AND SALT AS PRODUCTS.
