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Crank
3 years ago
9

The period of a pendulum T is assumed to depend only on the mass m, the length of the pendulum `, the acceleration due to gravit

y g, and the angle of swing θ. By means of dimensional analysis, simplify this problem and express this dependence in non dimensional terms.
Engineering
1 answer:
zzz [600]3 years ago
8 0

Answer:

The expression is shown in the explanation below:

Explanation:

Thinking process:

Let the time period of a simple pendulum be given by the expression:

T = \pi \sqrt{\frac{l}{g} }

Let the fundamental units be mass= M, time = t, length = L

Then the equation will be in the form

T = M^{a}l^{b}g^{c}

T = KM^{a}l^{b}g^{c}

where k is the constant of proportionality.

Now putting the dimensional formula:

T = KM^{a}L^{b}  [LT^{-} ^{2}]^{c}

M^{0}L^{0}T^{1} = KM^{a}L^{b+c}

Equating the powers gives:

a = 0

b + c = 0

2c = 1, c = -1/2

b = 1/2

so;

a = 0 , b = 1/2 , c = -1/2

Therefore:

T = KM^{0}l^{\frac{1}{2} } g^{\frac{1}{2} }

T = 2\pi \sqrt{\frac{l}{g} }

where k = 2\pi

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Answer:

8 to 10 times

Explanation:

For dry road

u= 15 mph        ( 1 mph = 0.44 m/s)

u= 6.7 m/s

Let take coefficient of friction( μ) of dry road is 0.7

So the de acceleration a = μ g

a= 0.7 x 10  m/s ²                         ( g=10 m/s ²)

a= 7 m/s ²

We know that

v= u - a t

Final speed ,v=0

0 = 6.7 - 7 x t

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For snow road

μ = 0.4

de acceleration a = μ g

a = 0.4 x 10 = 4 m/s ²

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We can say that it will take 8 to 10 times more time as compare to dry road for stopping the vehicle.

8 to 10 times

7 0
3 years ago
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A particle moving on a straight line has acceleration a = 5-3t, and its velocity is 7 at time t = 2. If s(t) is the distance fro
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Given acceleration a = 5-3t, and its velocity is 7 at time t = 2, the value of s2 - s1 = 7

<h3>How to solve for the value of s2 - s1</h3>

We have

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12+c-5+c = 0

7 = c

Read more on acceleration here: brainly.com/question/605631

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On aircraft equipped with fuel pumps, when is the auxiliary electric driven pump used?.
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Technician A says that hoods are designed with reinforcements to prevent folding during a collision. Technician B says that some
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Technician A is wrong.

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Technician B is right.

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...simplify devices, reducing weight and the chance of failure.

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