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Gnom [1K]
3 years ago
15

What is the moment of inertia i of this assembly about the axis through which it is pivoted?

Physics
1 answer:
vivado [14]3 years ago
7 0

Answer:

I = \frac{1}{12}m_t(2x)^2+m_1x^2+m_2x^2

Explanation:

The moment of inertia for the beam is:

I = \frac{1}{12}m_tL^2

Where m_t is the mass of the beam and L is the lengh of the beam

note:

L = 2x

And for particles I is equal to:

I = MR^2

where M is the mass of the particle and R is the distance between the pivot and the particle.

Finally, the moment of inertia for this assembly is the sum of the moment of inertia of the particles and the beam. So:

I = \frac{1}{12}m_t(2x)^2+m_1x^2+m_2x^2

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With 51 gallons of fuel in its tank, the airplane has a weight of 2390.7 pounds. What is the weight of the plane with 81 gallons
Shtirlitz [24]

Answer: 2561.7 pounds

Explanation:

If we assume the total weight of an airplane (in pounds units) as a <u>linear function</u> of the amount of fuel in its tank (in gallons) and we make a Weight vs amount of fuel graph, which resulting slope is 5.7, we can use the slope equation of the line:

m=\frac{Y-Y_{1}}{X-X_{1}}  (1)

Where:

m=5.7 is the slope of the line

Y_{1}=2390.7pounds is the airplane weight with  51 gallons of fuel in its tank (assuming we chose the Y axis for the airplane weight in the graph)

X_{1}=51gallons is the fuel in airplane's tank for a total weigth of 2390.7 pounds (assuming we chose the X axis for the a,ount of fuel in the tank in the graph)

This means we already have one point of the graph, which coordinate is:

(X_{1},Y_{1})=(51,2390.7)

Rewritting (1):

Y=m(X-X_{1})+Y_{1}  (2)

As Y is a function of X:

Y=f_{(X)}=m(X-X_{1})+Y_{1}  (3)

Substituting the known values:

f_{(X)}=5.7(X-51)+2390.7  (4)

f_{(X)}=5.7X-290.7+2390.7  (5)

f_{(X)}=5.7X+2100  (6)

Now, evaluating this function when X=81 (talking about the 81 gallons of fuel in the tank):

f_{(81)}=5.7(81)+2100  (7)

f_{(81)}=2561.7  (8)   This means the weight of the plane when it has 81 gallons of fuel in its tank is 2561.7 pounds.

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