Answer:
Explanation:
The path length difference = extra distance traveled
The destructive interference condition is:
where m =0,1, 2,3........
So, ←
![\Delta d = (m+1/2)\lamb da9/tex]so [tex]\Delta d = \frac{\lambda}{2}](https://tex.z-dn.net/?f=%5CDelta%20d%20%3D%20%28m%2B1%2F2%29%5Clamb%20da9%2Ftex%5D%3C%2Fstrong%3E%3C%2Fp%3E%3Cp%3E%3Cstrong%3Eso%20%3C%2Fstrong%3E%5Btex%5D%5CDelta%20d%20%3D%20%5Cfrac%7B%5Clambda%7D%7B2%7D)
⇒ λ = 2Δd = 2×10 = 20
Answer:
The motion is over-damped when λ^2 - w^2 > 0 or when 
> 0.86
The motion is critically when λ^2 - w^2 = 0 or when = 0.86
The motion is under-damped when λ^2 - w^2 < 0 or when < 0.86
Explanation:
Using the newton second law
k is the spring constante
b positive damping constant
m mass attached
x(t) is the displacement from the equilibrium position
Converting units of weights in units of mass (equation of motion)
From hook's law we can calculate the spring constant k
If we put m and k into the DE, we get
Denoting the constants
2λ = 
= 
λ = b/0.215
λ^2 - w^2 = 
This way,
The motion is over-damped when λ^2 - w^2 > 0 or when > 0.86
The motion is critically when λ^2 - w^2 = 0 or when = 0.86
The motion is under-damped when λ^2 - w^2 < 0 or when < 0.86
Answer:
691200 J
Explanation:
From specific heat capacity,
ΔQ = cmΔt.................. Equation 1
Where ΔQ = increase in thermal energy, c = specific heat capacity of the body, m = mass of the man, Δt = rise in temperature.
Given: c = 3.6 kJ/kg.°C = 3600 J/kg.°C, m = 96 kg, Δt = 39-37 = 2 °C.
Substitute into equation 1
ΔQ = 3600×96×2
ΔQ = 691200 J.
Hence the change in the thermal energy of the body = 691200 J
Answer:
θ = 13.16 °
Explanation:
Lets take mass of child = m
Initial velocity ,u= 1.1 m/s
Final velocity ,v=3.7 m/s
d= 22.5 m
The force due to gravity along the incline plane = m g sinθ
The friction force = (m g)/5
Now from work power energy
We know that
work done by all forces = change in kinetic energy
( m g sinθ - (m g)/5 ) d = 1/2 m v² - 1/2 m u²
(2 g sinθ - ( 2 g)/5 ) d = v² - u²
take g = 10 m/s²
(20 sinθ - ( 20)/5 ) 22.5 = 3.7² - 1.1²
20 sinθ - 4 =12.48/22.5
θ = 13.16 °
For #5 It's helpful to draw a free body diagram so you know which way the forces are acting on the block.
the weight mg is acting downwards, and you need to find the vertical and horizontal components of mg using sin and cosine. so do 15x9.8xsin40 which is the force. Assuming no friction, this is the only force acting on the block, as the forces on the vertical plane cancel out i.e the normal force and weight of the block.
after, just do F=ma And since you know F and m, solve for a.
