Answer: a) v = ω /k, b) v = - ωAcos( kx −ωt)
Explanation:
y(x,t)=Asin(kx−ωt) defines the wave equation.
a)
We are asked to find wave speed (v)
Recall that v = fλ
From the wave equation above,
k = 2π/ λ where k is the wave number and λ is the wavelength, λ = 2π /k
ω = 2πf where f is the frequency and ω is the angular frequency.
f = ω/ 2π.
By substituting for λ and ω into the wave speed formulae, we have that
v =( ω/ 2π) × (2π /k)
v = ω/k
b)
y(x,t)=Asin(kx−ωt)
The first derivative of y with respect to x give the velocity (vy)
By using chain rule, we have that
v = dy/dt = A cos( kx −ωt) × (−ω)
v = - ωAcos( kx −ωt)
Intermolecular forces are forces that keep molecules together. For example, the forces between two water molecules. The stronger the intermolecular forces are, the more "solid" is the matter going to be, meaning that the intermolecular forces are the strongest in solids and weakest in gases.
Make sure not to confuse intERmolecular forces (forces between *molecules*) and intRAmolecular forces (forces between *atoms* that make up a molecule).
Reactions occur when two or more molecules interact and the molecules change. Bonds between atoms are broken and created to form new molecules. That's it.
Forces are needed to lift, turn, move, open, close, push, pull, and so on. When you throw a ball, you are using force to make the ball move through the air. More than one force can act on an object at the same time.
Answer:
d = 0.05 [m] = 50 [mm]
Explanation:
We must remember the principle of conservation of energy which tells us that energy is transformed from one way to another. For this case, the initial kinetic energy is transformed into useful work that is equal to the product of force by distance.
![E_{k}=F*d\\400 = 8000*d\\d = 0.05 [m] = 50 [mm]](https://tex.z-dn.net/?f=E_%7Bk%7D%3DF%2Ad%5C%5C400%20%3D%208000%2Ad%5C%5Cd%20%3D%200.05%20%5Bm%5D%20%3D%2050%20%5Bmm%5D)
