A spring oscillator is designed with a mass of 0.231 kg. It operates while immersed in a damping fluid, selected so that the oscillation amplitude will decrease to 1.00% of its initial value in 9.43 s. Find the required damping constant for the system.

Answers

Answer 1
Answer:

Answer:

.487 s⁻¹

Explanation:

Let damping constant be τ . The equation of decreasing amplitude can be written as

A = A₀ e^{-\tau t

A / A₀ = e^{-\tau t

At t = 9.43 s , A / A₀ = .01

.01 = [e^{-\tau*9.43

ln.01 = - 9.43 τ

-4.6 = -9.43τ

τ = .487 s⁻¹

Answer 2
Answer:

Answer:

0.05508 kg/sec

Explanation:

mass of the oscillator m= 0.231 Kg

amplitude of oscillation given by

A=A_0e^(-It)

Ao= maximum amplitude

t= time and  1.00% of its initial value in t= 9.43 s.

A= 0.01Ao

⇒0.01=e^(-I×9.43)

ln100= 9.43×l

l=0.4883

we know that l= c/2m

c= damping constant

c= 2ml

=2×0.231×0.4883

=0.05508 kg/sec


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Suppose you left a 100-W light bulb on continuously for one month. If the electricity generation and transmission efficiency is 30%, how much chemical energy (in joules) was wasted at the power plant for this oversight? If the fuel consumption for one meal in Cambodia using a kerosene wick stove is 6 MJ (1 MJ = 1,000,000 joules), how many equivalent meals could be cooked with this wasted energy.

Answers

The wasted chemical energy be "8.64 × 10⁸ J" and the equivalent meals could be cooked be "144".

Chemical energy

According to the question,

Bulb power, P = 100 W

Time, t = 1 month or,

            = 1 × 30 × 24

            = 720 h

Efficiency, η = 30% or,

                     = 0.30

Fuel consumption, E = 6 MJ or,

                                   = 6 × 10⁶ J  

Energy consumed be:

E_c = P × t

By substituting the values,

       = 100 × 720

       = 72 kWh

Wasted energy be:

E_g = (E_c)/(\eta)

       = (72000)/(0.3)

       = 240 kWh or,

       = 240 × 3.6 × 10⁶

       = 8.64 × 10⁸ J

and,

The no. of meals be:

→ N = (8.64* 10^8)/(6* 10^6)

      = 144 meals

Thus the answers above are correct.      

Find out more information about chemical energy here:

brainly.com/question/347340

Answer:

a

 E_g  =  240 \  kWh

b

N =  144 \  meals

Explanation:

From the question we are told that

The power rating of the bulb is P = 100 W

The duration is t = 1 month = 1 * 30 * 24 = 720 h

The efficiency is \eta  =  30\% =  0.30

The fuel consumption for one meal is E =  6 MJ  =  6 *10^6 J

Generally the energy consumed by the bulb is mathematically represented as

E_c  =  P * t

=> E_c  =  100 * 720

=> E_c  =  72\ k Wh

Generally the energy generated at the power plant that was wasted by the bulb is mathematically represented as

E_g  =  (E_c)/(\eta)

=> E_g  =  (72000)/(0.3)

=> E_g  =  240 \  kWh

Converting this value  to  Joules

       E_g  =  240  *   3.6 * 10^(6)  =  8.64*10^8

Generally the number of means that would be cooked is

N =  (8.64*10^8 )/(6 *10^6)

=>    N =  144 \  meals

A rock is thrown vertically upward with a speed of 14.0 m/sm/s from the roof of a building that is 70.0 mm above the ground. Assume free fall.A) In how many seconds after being thrown does the rock strike the ground? B) What is the speed of the rock just before it strikes the ground?

Answers

Answer:

(A). The time is 5.47 sec.

(B). The speed of the rock just before it strikes the ground is 39.59 m/s.

Explanation:

Given that,

Initial velocity = 14.0 m/s

Height = 70.0 m

(A). We need to calculate the time

Using second equation of motion

s=ut+(1)/(2)gt^2

Put the value into the formula

70=-14* t+(1)/(2)*9.8* t^2

4.9t^2-14t-70=0

t =5.47\ sec

(B). We need to calculate the speed of the rock just before it strikes the ground

Using third equation of motion

v^2=u^2+2gs

Put the value into the formula

v^2=(14)^2+2*9.8*70

v^2=1568

v=√(1568)

v=39.59\ m/s

Hence, (A). The time is 5.47 sec.

(B). The speed of the rock just before it strikes the ground is 39.59 m/s.

You observe three carts moving to the right. Cart A moves to the right at nearly constant speed. Cart B moves to the right, gradually speeding up. Cart C moves to the right, gradually slowing down. Which cart or carts, if any, experience a net force to the right

Answers

Answer:

Explanation:

Cart A is moving to the right with constant speed i.e. net acceleration is zero

because acceleration is change in velocity in given time

Cart B is moving towards right with gradually speed up so there is net acceleration which helps to increase the velocity s

This indicates the net force acting on the cart towards right

For cart C there is gradual slow down of cart which indicates cart is decelerating and a net force is acting towards which opposes its motion.

A test charge of 13 mC is at a point P where an external electric field is directed to the right and has a magnitude of 4 3 106 N/C. If the test charge is replaced with another test charge of 23 mC, what happens to the external electric field at P

Answers

Answer:

The magnitude of the external electric field at P will reduce to 2.26 x 10⁶ N/C, but the direction is still to the right.

Explanation:

From coulomb's law, F = Eq

Thus,

F = E₁q₁

F = E₂q₂

Then

E₂q₂ = E₁q₁

E_2 = (E_1q_1)/(q_2)

where;

E₂ is the external electric field due to second test charge = ?

E₁ is the external electric field due to first test charge = 4 x 10⁶ N/C

q₁ is the first test charge = 13 mC

q₂ is the second test charge = 23 mC

Substitute in these values in the equation above and calculate E₂.

E_2 = (4*10^6*13)/(23) = 2.26 *10^6 \ N/C

The magnitude of the external electric field at P will reduce to 2.26 x 10⁶ N/C when 13 mC test charge is replaced with another test charge of 23 mC.

However, the direction of the external field is still to the right.

Circuit A in a house has a voltage of 218 V and is limited by a 45-A circuit breaker. Circuit B is at 120.0 V and has a 25-A circuit breaker.What is the ratio of the maximum power delivered by circuit A to that delivered by circuit B?

Answers

Answer:

3.27

Explanation:

Electric Power: This can be defined as the rate at which electric energy is consumed. The unit of power is Watt (W).

Mathematically, electric power is represented as

P = VI ..................................... Equation 1.

Where P = power, V = voltage, I = Current.

For Circuit A,

P₁ = V₁I₁ ................................... Equation 2

Where P₁ = maximum power delivered by circuit A, V₁ = Voltage of circuit A, I₁ = circuit breaker rating of circuit A.

Given: V₁ = 218 V, I₁ = 45 A.

Substituting into equation 2

P₁ = 218×45

P₁  = 9810 W.

For Circuit B,

P₂ = V₂I₂............................. Equation 3

Where P₂ = maximum power delivered by the circuit B, V₂ = voltage of circuit B, I₂ = circuit breaker rating of circuit B

Given: V₂ = 120 V, I₂ = 25 A.

Substitute into equation 3

P₂ = 120(25)

P₂ = 3000 W.

Ratio of maximum power delivered by circuit A to that delivered by circuit B = 9810/3000

= 3.27.

Thus the ratio of maximum power delivered by circuit A to circuit B = 3.27

Which of these factors make hydrogen fuel cells a better option than burning fossil fuels? A.Hydrogen fuel cells have a higher energy efficiency. B.Hydrogen fuel cells create less pollution. C.Burning fossil fuels relies on outdated devices and technology. D.Hydrogen is the most abundant element in the universe. E.Hydrogen fuel cells are more expensive than fossil fuels.

Answers

Answer: i think it is B

Explanation: