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DaniilM [7]
4 years ago
9

A simple pendulum, consisting of a mass on a string of length L, is undergoing small oscillations with amplitude A.

Physics
1 answer:
Leya [2.2K]4 years ago
4 0

Answer:

A. Period is halved

Explanation:

The period of a pendulum swing, T, is given in terms of mass as:

T = 2\pi \sqrt{\frac{I}{mgL} }

where I = moment of inertia

m = mass of the pendulum

g = acceleration due to gravity

h = Length of string

If the mass is increased by a factor of 4, that means:

M = 4m

(M = new mass)

The new period of the pendulum, T_n, will now be:

T_n = 2\pi \sqrt{\frac{I}{MgL} }\\\\\\T_n = 2\pi \sqrt{\frac{I}{4mgL} }\\\\\\T_n = 2\pi \sqrt{\frac{1}{4} * \frac{I}{mgL} }\\\\\\T_n = \frac{2\pi}{2}  \sqrt{\frac{I}{mgL} }\\\\\\T_n = \frac{1}{2} * 2\pi \sqrt{\frac{I}{mgL} }\\\\\\T_n = \frac{1}{2} * T

Hence, the period is halved.

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Answer:

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Note: the composition of a pure substance is fixed, but the composition of a mixture can vary. Two salt water solutions might not have the same concentration of salt. Or, if you prefer, one blueberry muffin might have more blueberries in it than another blueberry muffin.

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5 0
4 years ago
An air-track glider undergoes a perfectly inelastic collision with an identical glider that is initially at rest. what fraction
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Refer to the diagram shown below.

The initial KE (kinetic energy) of the system is
KE₁ = (1/2)mu²

After an inelastic collision, the two masses stick together.
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3 years ago
What happens to molecules when heat is absorbed in a substance
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3 years ago
A rectangular tank that is 4 feet long, 2 feet wide and 15 feet deep is filled with a heavy liquid that weighs 60 pounds per cub
V125BC [204]

Answer:

a) W₁ = 54000 Lb-ft

b) W₂ = 77760 Lb-ft

c)  W₃ = 24000 Lb-ft

W₄ = 40560 Lb-ft

Step by step

W= ∫₁² ydF         1  and  2 are the levels of liquid

Where dF is the differential of weight of a thin layer

y is the height of the differential layer and

ρ*V  = F

Then

dF = ρ* A*dy*g

ρ*g  =  60 lb/ft³

A= Area of the base then

Area of the base is:

A(b) = 4*2  =  8 ft²

Now we have the liquid weighs  60 lb/ft³

Then the work is:

a)

   W₁ = ∫₀¹⁵ 8*60*y*dy     ⇒   W₁ =480* ∫₀¹⁵ y*dy

W₁ =480* y² /2 |₀¹⁵      ⇒  480/2 [ (15)² - 0 ]

W₁ = 240*225

W₁ = 54000 Lb-ft

b) The same expression, but in this case we have to pump 3 feet higher, then:

W₂ = ∫₀¹⁸ 480*y*dy     ⇒ 480*∫₀¹⁸ydy    ⇒ 480* y²/2 |₀¹⁸

W₂ =  480/2 * (18)²

W₂ =  240*324

W₂ = 77760 Lb-ft

c) To pump two-thirds f the liquid we have

2/3* 15  =  10

W₃ = 480*∫₀¹⁰ y*dy   ⇒  W₃ = 480* y²/2 |₀¹⁰

W₃ = 240*(10)²

W₃ = 24000 Lb-ft

d)

W₄ =480*∫₀¹³ y*dy

W₄ =480* y²/2 |₀¹³

W₄ = 240*(13)²

W₄ = 240*169

W₄ = 40560 Lb-ft

3 0
3 years ago
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