A) 140 degrees
First of all, we need to find the angular velocity of the Ferris wheel. We know that its period is
T = 32 s
So the angular velocity is
Assuming the wheel is moving at constant angular velocity, we can now calculate the angular displacement with respect to the initial position:
and substituting t = 75 seconds, we find
In degrees, it is
So, the new position is 140 degrees from the initial position at the top.
B) 2.7 m/s
The tangential speed, v, of a point at the egde of the wheel is given by
where we have
r = d/2 = (27 m)/2=13.5 m is the radius of the wheel
Substituting into the equation, we find
The percentage of light gets through three successive polarized filters is 24.9 %
From the question,
Given that,
Angle of transmission axis = 32.8°
The intensity of light emerging from the first polarizer is determined by the equation
I₁ = I₀ / 2
where I₀ ⇒ intensity of unpolarized light
The light emerging from the second polarizer can be mathematically represented by,
I₂ = I₁ x cos²θ
Substituting the values,
I₂ =( I₀/2) x cos²θ
= (I₀/2) x cos² (32.8 )
= (I₀/2) x 0.706
= (0.706 / 2 ) x I₀
The light emerging from the third polarizer is represented as,
I₃ = I₂ x cos²θ
Substituting the values in the above equation,
I₃ = ( 0.706 / 2 ) I₀ x cos² (32.8)
= (0.706 / 2 ) I₀ x 0.706
= 0.249 I₀
The percentage of intensity of light that gwts through with respect to the intensity of unpolarized light is given by the equation,
(I₃ / I₀) x 100
Substituting the values
[(0.249 x I₀) / I₀ ] x 100 = 24.9 %
Hence the percentage of light gets through is 24.9%
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The resultant force is 8N
Given that mass is 2kg , v= 40m/s, u =20m/s and we need to calculate resultant force
F=ma
m is given
so for a
v-u/t=a { first equation of motion }
40-20/4= 4
so a=4
F = ma =2*4 = 8N
The difference between the forces that are acting on an object as part of a system is known as the resultant force.
v = u + at is the first equation of motion. Here, v denotes the end speed, u the starting speed, an acceleration, and t the passage of time. The first equation of motion is provided by the velocity-time relation, which may be used to calculate acceleration.
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Complete question is;
The place you get your hair cut has two nearly parallel mirrors 6.50 m apart. As you sit in the chair, your head is 3.00 m from the nearer mirror. Looking toward this mirror, you first see your face and then, farther away, the back of your head. (The mirrors need to be slightly nonparallel for you to be able to see the back of your head, but you can treat them as parallel in this problem.) How far away does the back of your head appear to be?
Answer:
13 m
Explanation:
We are given;
Distance between two nearly parallel mirrors; d = 6.5 m
Distance between the face and the nearer mirror; x = 3 m
Thus, the distance between the back-head and the mirror = 6.5 - 3 = 3.5m
Now, From the given values above and using the law of reflection, we can find the distance of the first reflection of the back of the head of the person in the rear mirror.
Thus;
Distance of the first reflection of the back of the head in the rear mirror from the object head is;
y' = 2y
y' = 2 × 3.5
y' = 7
The total distance of this image from the front mirror would be calculated as;
z = y' + x
z = 7 + 3
z = 10
Finally, the second reflection of this image will be 10 meters inside in the front mirror.
Thus, the total distance of the image of the back of the head in the front mirror from the person will be:
T.D = x + z
T.D = 3 + 10
T.D = 13m
The law applied here is Hooke's Law which describes the force exerted by the spring with a given distance. The equation for this is F = kΔx, where F is the force in Newtons, k is the spring constant in N/m while Δx is the displacement in meters.
If you want to find work done by a spring, this can be solved by using differential equations. However, derived equations are already ready for use. The equation is
W = k[{x₂-x₁)² - (x₁-xn)²],
where
xn is the natural length
x₁ is the stretched length
x₂ is also the stretched length when stretched even further than x₁
In this case xn =x₁. So, that means that (x₁-xn) = 0 and (x₂-x₁) = 11 cm or 0.11 m.
Then, substituting the values,
2 J = k (0.11² -0²)
k = 165.29 N/m
Finally, we use the value of k to the Hooke's Law to determine the Force.
F = kΔx = (165.29 N/m)(0.11 m)
F = 18.18 Newtons
