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Klio2033 [76]
3 years ago
7

Consider a block of mass m attached to two springs, one on the left with spring constant k1 and one on the right with spring con

stant k2. Each spring is attached on the other side to a wall, and the block slides without friction on a horizontal surface. When the block is sitting at x = 0, both springs are relaxed. Write Newton’s second law, F = ma, as a differential equation for an arbitrary position x of the block. What is the period of oscillation of this system?
Physics
1 answer:
Andrew [12]3 years ago
3 0

Answer:

T= 2\pi\times sqrt(m/(k1+k2))

Explanation:

When the block is displaced by x units

F= spring force

two springs are connected parallel

F =-k_1x - k_2x

Writing Newtons second law, F = ma

-k_1x - k_2x =ma

-k_1x - k_2x = mx''

a= x" ( differentiating x w.r.t time twice)

x''+(k_1/m + k_2/m) x=0

this the standard form of equation of oscillation spring mass system

This is the differential equation, x'' means that double differentiation of x , i.e, x'' is acceleration

since,  Period T=2\pi\sqrt{\frac{m}{K_{eq.}} }

therefore,

T= 2\pi\times sqrt(m/(k1+k2))

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Answer:

20.0 cm

Explanation:

Here is the complete question

The normal power for distant vision is 50.0 D. A young woman with normal distant vision has a 10.0% ability to accommodate (that is, increase) the power of her eyes. What is the closest object she can see clearly?

Solution

Now, the power of a lens, P = 1/f = 1/u + 1/v where f = focal length of lens, u = object distance from eye lens and v = image distance from eye lens.

Given that we require a 10 % increase in the power of the lens to accommodate the image she sees clearly, the new power P' = 50.0 D + 10/100 × 50 = 50.0 D + 5 D = 55.0 D.

Also, since the object is seen clearly, the distance from the eye lens to the retina equals the distance between the image and the eye lens. So, v = 2.00 cm = 0.02 m

Now, P' = 1/u + 1/v

1/u = P'- 1/v

1/u = 55.0 D - 1/0.02 m

1/u = 55.0 m⁻¹ - 1/0.02 m

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1/u = 5.0 m⁻¹

u = 1/5.0 m⁻¹

u = 0.2 m

u = 20 cm

So, at 55.0 dioptres, the closet object she can see is 20 cm from her eye.

8 0
2 years ago
A gas has an initial volume of 2.5 L at a temperature of 275 K and a pressure of 2.1 atm. The pressure of the gas increases to 2
olchik [2.2K]

Answer:

2.10L

Explanation:

Given data

V1= 2.5L

T1= 275K

P1= 2.1atm

P2= 2.7 atm

T2= 298K

V2= ???

Let us apply the gas equation

P1V1/T1= P2V2/T2

substitute into the expression we have

2.1*2.5/275= 2.7*V2/298

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275*2.7V2= 298*5.25

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V2= 1564.5/742.5

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Nonconjugated β,γ-unsaturated ketones are in base-catalyzed equilibrium with their conjugated α,β-unsaturated isomers. The mecha
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Answer:

Explanation:

The equilibrium mechanism for the reversible acid is catalyzed by the isomerization of non conjugated β, γ- unsaturated ketones, like 3-cyclohexanone to their conjugated α, I²- unsaturated isomers.

Oxygen of the Carbonyl group in the ketone is protonated by the acid and this is followed by the abstraction of an α- hydrogen from the protonated 3-cyclo hexanone to yield ethanol

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irakobra [83]

Answer:

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The generator uses fuel to cause the mechanical motion of the pistons in the device.

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