T sin θ = M g = W cable supporting weight
T = 100 * 9.8 / sin 40 = 1525 N
T cos θ = Th horizontal force due to cable
Th = 1525 cos 40 = 1168 N
Answer:
The critical angle for light is 41.81 degrees.
Explanation:
We have, light is propagating from a material with index of refraction of 1.50 to a material with index of refraction of 1. It is required to find the critical angle for light. It is angle for which the angle of refraction is equal to 90 degrees. It is given by :
So, the critical angle for light is 41.81 degrees.
Answer:
This is a very straightforward problem, and not too difficult to do in your head. If we have two nearly equal resistances, the series resistance (Rs) is twice the average value (midpoint between the two) and the parallel resistance Rp) is approximately equal to half the midpoint value. So a rough initial guess might be 12 and 13 ohms, where Rs is 25 ohms but Rp is approximately 6.25 ohms. Since Rp needs to be lower, we can play around with resistor values. Here’s an easy shortcut:
Let’s start with the equation for two parallel resistors:
Rp = (R1 * R2)/(R1 + R2)
Since Rs = R1 + R2,
Rp = (R1 * R2)/Rs.
We can rewrite this as
Rp * Rs = R1 * R2
Plugging in our numbers (Rp = 6, Rs = 25), we see that R1 + R2 = 150. What two numbers in the vicinity of 12 and 13 have the product of 150 and a sum of 25? Immediately 10 and 15 come to mind! Easy enough!
Answer:
(ω₁ / ω₂) = 1.9079
Explanation:
Given
R₁ = 3.59 cm
R₂ = 7.22 cm
m₁ = m₂ = m
K₁ = K₂
We know that
K₁ = Kt₁ + Kr₁ = 0.5*m₁*v₁²+0.5*I₁*ω₁²
if
v₁ = ω₁*R₁
and
I₁ = (2/3)*m₁*R₁² = (2/3)*m*R₁²
∴ K₁ = 0.5*m*ω₁²*R₁²+0.5*(2/3)*m*R₁²*ω₁² <em>(I)</em>
then
K₂ = Kt₂ + Kr₂ = 0.5*m₂*v₂²+0.5*I₂*ω₂²
if
v₂ = ω₂*R₂
and
I₂ = 0.5*m₂*R₂² = 0.5*m*R₂²
∴ K₂ = 0.5*m*ω₂²*R₂²+0.5*(0.5*m*R₂²)*ω₂² <em>(II)</em>
<em>∵ </em>K₁ = K₂
⇒ 0.5*m*ω₁²*R₁²+0.5*(2/3)*m*R₁²*ω₁² = 0.5*m*ω₂²*R₂²+0.5*(0.5*m*R₂²)*ω₂²
⇒ ω₁²*R₁²+(2/3)*R₁²*ω₁² = ω₂²*R₂²+0.5*R₂²*ω₂²
⇒ (5/3)*ω₁²*R₁² = (3/2)*ω₂²*R₂²
⇒ (ω₁ / ω₂)² = (3/2)*R₂² / ((5/3)*R₁²)
⇒ (ω₁ / ω₂)² = (9/10)*(7.22/ 3.59)²
⇒ (ω₁ / ω₂) = (7.22/ 3.59)√(9/10)
⇒ (ω₁ / ω₂) = 1.9079
