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Lyrx [107]
3 years ago
5

A. What is the equation describing the motion of a mass on the end of a spring which is stretched 8.8cm from equilibrium and the

n released from rest, and whose period is 0.66s? Assume that the displacement at the start of the motion is positive. (express your answer in terms of t using two significant figures.)
B. What will be its displacement after 1.7s? (express your answer to two significant figures and include the appropriate units.)
Physics
2 answers:
Naddik [55]3 years ago
5 0

Answer:

a) x = 8.8 cm * cos (9.52 rad/s * t)

b) x = 8.45 cm

Explanation:

This is a Simple Harmonic Motion, and most Simple Harmonic Motion equations start from the equilibrium point. In this question however, we are starting from the max displacement the equations, and thus, it ought to be different.

From the question, we are given that

A = 8.8 cm = 0.088 m

t = 0.66 s

Now, we need to find the angular speed w, such that

w = 2π/T

w = (2 * 3.142) / 0.66

w = 6.284 / 0.66

w = 9.52 rad/s

The displacement equation of Simple Harmonic Motion is usually given as

x = A*sin(w*t)

But then, the equation starts from the equilibrium point at 0 sec, i.e x = 0 m

When you have to start from the max displacement, then the equation would be

x = A*cos(w*t).

So when t = 0 the cos(0) = 1, and then x = A which is max displacement.

Thus, the equation is

x = 8.8 cm * cos (9.52 rad/s * t)

At t = 1.7 s,

x = 8.8 cos (9.52 * 1.7)

x = 8.8 cos (16.184)

x = -8.45 cm

Jobisdone [24]3 years ago
3 0

Answer:  

(a)      $y(t) = 8.8cos(\frac{2\pi }{0.665} t)$

(b)  and after 1.7s the displacement would be

$y(1.7s) = 8.8cos(\frac{2\pi }{0.665s}1.7s)$ = 8.456461cm

Explanation:

This is periodic motion and the best equation to model this type of motion is sinusoidal equation.

We will chose cos function because it starts at the max or the amplitude.

A = 8.8cm, T = 0.66s in following general form gives the answer.

$y(t)=Acos(\frac{2\pi }{T} t)

and substituting t = 1.7s in it gives us 8.456461cm, just little bit lower than initial position.

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A,b, e are complete. Help on the others would be so appreciated!!
bixtya [17]

Answer:

serie Ceq=0.678 10⁻⁶ F  and the charge Q = 9.49 10⁻⁶ C

Explanation:

Let's calculate all capacity values

a) The equivalent capacitance of series capacitors

    1 / Ceq = 1 / C1 + 1 / C2 + 1 / C3 + 1 / C4 + 1 / C5

    1 / Ceq = 1 / 1.5 + 1 / 3.3 + 1 / 5.5 + 1 / 6.2 + 1 / 6.2

    1 / Ceq = 1 / 1.5 + 1 / 3.3 + 1 / 5.5 + 2 / 6.2

    1 / Ceq = 0.666 + 0.3030 +0.1818 +0.3225

    1 / Ceq = 1,147

    Ceq = 0.678 10⁻⁶ F

b) Let's calculate the total system load

   Dv = Q / Ceq

   Q = DV Ceq

   Q = 14 0.678 10⁻⁶

   Q = 9.49 10⁻⁶ C

In a series system the load is constant in all capacitors, therefore, the load in capacitor 5.5 is Q = 9.49 10⁻⁶ C

c) The potential difference

   ΔV = Q / C5

   ΔV = 9.49 10⁻⁶ / 5.5 10⁻⁶

   ΔV = 1,725 ​​V

d) The energy stores is

    U = ½ C V²

    U = ½ 0.678 10-6 14²

    U = 66.4 10⁻⁶ J

e) Parallel system

   Ceq = C1 + C2 + C3 + C4 + C5

   Ceq = (1.5 +3.3 +5.5 +6.2 +6.2) 10⁻⁶

   Ceq = 22.7 10⁻⁶ F

f) In the parallel system the voltage is maintained

   Q5 = C5 V

   Q5 = 5.5 10⁻⁶ 14

   Q5 = 77 10⁻⁶ C

g) The voltage is constant V5 = 14 V

h) Energy stores

   U = ½ C V²

   U = ½ 22.7 10-6 14²

   U = 2.2 10⁻³ J

8 0
3 years ago
Light of wavelength 559 nm is used to illuminate normally two glass plates 22.1 cm in length that touch at one end and are separ
umka21 [38]

Answer:

M = 222 fringes

Explanation:

given

λ = 559 n m = 559 × 10⁻⁹ m

radius = 0.026 mm = 0.026 ×10⁻³ m

length of the glass plate = 22.1 ×10⁻² m

using relation

2t=(m+\dfrac{1}{2})\lambda\ \ (m=0,1,2,3...)\\where\ 0\leq t\leq 2r\\m = \dfrac{2t}{\lambda}-\dfrac{1}{2}

m_{max} = \dfrac{2\times 2r}{\lambda}-\dfrac{1}{2}\\m_{max} = \dfrac{2\times 2\times 0.026\times 10^{-3}}{559\times 10^{-9}}-\dfrac{1}{2}

 = 221.79  

 = 221 (approx.)

hence no of bright fringe

M = m + 1

   = 221 +1

M = 222 fringes

6 0
3 years ago
2) A motorcycle is moving at a constant speed of 40 km/h. How long does it take the motorcycle to
docker41 [41]

Answer:

2 hours

Explanation:

The motorcycle travels 40 km per hour.

80km / 40km/h = 2 hours.

7 0
4 years ago
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Pounds

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Which best summarizes a concept related to the work-energy theorem?
Maurinko [17]

Answer:

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Explanation:

According to the work-energy theorem, the net work done by the forces on a body or an object is equal to the change produced in the kinetic energy of the body or an object.

The concept that summarizes a concept related to the work-energy theorem is that ''When work is positive, the environment does work on an object.''

4 0
3 years ago
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