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RSB [31]
3 years ago
12

A spring with an 8-kg mass is kept stretched 0.4 m beyond its natural length by a force of 32 N. The spring starts at its equili

brium position and is given an initial velocity of 4 m/s. Find the position of the mass at any time t. (Use x for the displacement in meters from the equilibrium position.)
Physics
2 answers:
pentagon [3]3 years ago
7 0

Answer:

x = 1.26 sin 3.16 t

Explanation:

Assume that the general equation of the displacement given as

x = A sinω t

A=Amplitude ,t=time ,ω=natural frequency

We know that speed V

V=\dfrac{dx}{dt}

V= A ω cosωt

Maximum velocity

V(max)= Aω

Given that F= 32 N

F = K Δ

K=Spring constant

Δ = 0.4 m

32 =0.4 K

K = 80 N/m

We know that  ω²m = K

8 ω² = 80

ω = 3.16 s⁻¹

Given that V(max)= Aω = 4 m/s

3.16 A = 4

A= 1.26 m

Therefore the general equation of displacement

x = 1.26 sin 3.16 t

Colt1911 [192]3 years ago
4 0

Answer:

Explanation:

mass, m = 8 kg

extension, y = 0.4 m

force, F = 32 N

maximum velocity, v = 4 m/s

maximum velocity , v = ω A

where, ω be the angular velocity and A be the amplitude

4 = ω x 0.4

ω = 10 rad/s

position

x = A Sin ωt

x = 0.4 Sin 10 t

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A technician builds an RLC series circuit which includes an AC source that operates at a fixed frequency and voltage. At the ope
MariettaO [177]

Answer:

Xc = (0.467 - 0.427j)R

Explanation:

Since the resistance in the circuit is R, the reactance of the inductor is XL and the reactance of the capacitor is XC, then the impedance of the circuit is

Z = √[R² + (XL - XC)²]

Since the inductive reactance XL equals the resistance R, we have that

Z = √[R² + (XL - XC)²]

Z = √[R² + (R - XC)²]

Thus, the current in the circuit is thus I = V/Z = V/√[R² + (R - XC)²]

Now, when the plate separation of the parallel plate capacitor is reduced to one-half its original value, the current doubles. Also, when the plate separation is reduced to half, the capacitance doubles since C ∝ 1/d where C is capacitance and d separation between the plates. Since the capacitance doubles, the new reactance XC' is twice the initial reactance XC. So, XC' = 2XC. Thus the new impedance is thus

Z' = √[R² + (R - XC')²]

Z' = √[R² + (R - 2XC)²]

The new current is I' = V/Z' = V/√[R² + (R - 2XC)²]

Since the current doubles, I' = 2I.

V/√[R² + (R - 2XC)²] = 2V/√[R² + (R - XC)²]

1/√[R² + (R - 2XC)²] = 2/√[R² + (R - XC)²]

√[R² + (R - XC)²] = 2√[R² + (R - 2XC)²]

squaring both sides, we have

[R² + (R - XC)²] = 4[R² + (R - 2XC)²]

expanding the brackets, we have

[R² + R² - 2RXC + XC²] = 4[R² + R² - 4RXC + 4XC²]

[2R² - 2RXC + XC²] = 4[2R² - 4RXC + 4XC²]

2R² - 2RXC + XC² = 8R² - 16RXC + 16XC²

collecting like terms, we have

16RXC - 2RXC + XC² - 16XC² = 8R² - 2R²

14RXC - 15XC² = 6R²

15XC² - 14RXC + 6R² = 0

Using the quadratic formula to find XC, we have

XC = \frac{-(-14R) +/- \sqrt{(-14R)^{2} - 4 X 15 X 6R^{2} } }{2 X 15}\\= \frac{-(-14R) +/- \sqrt{196R^{2} - 360R^{2} } }{30}\\ \\= \frac{14R +/- \sqrt{- 164R^{2} } }{30}\\ \\= \frac{14R +/- 12.81Ri }{30}\\\\= 0.467R +/- 0.427Ri

Since it is capacitive, we take the negative part.

So, Xc = (0.467 - 0.427j)R

4 0
3 years ago
3.7 kg of a saturated water vapor at 0.4 MPa is isothermally cooled until it is a saturated liquid. Calculate the amount of heat
kirill115 [55]

Answer:

7.894 MJ

Explanation:

Given that:

The mass of the saturated water vapor = 3.7 kg

The pressure of the saturated water vapor = 0.4 MPa

From saturated properties of steam tables when the pressure is at 0.4 Mpa

The enthalpy in (kJ/kg);

hf = 604.7 kJ/kg

hg = 2738.1 kJ/kg

The rejected heat during this process is:

Q = m(hg - hf)

Q = 3.7(2738.1 - 604.7) kJ/kg

Q = 3.7(2133.4) kJ/kg

Q = 7893.58 kJ/kg

Q = 7.894 MJ

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Why does the band of stability curve upward at high atomic numbers? excess neutrons are required due to the repulsion between th
ella [17]
The band of stability curves upward at high atomic numbers due to the fact that excess of neutrons are required due to the repulsion between protons.

Atomic number is the number of protons. As the number of protons (atomic number) increase, the electrical repulsion force, due to the same sign of the protons inside the nucleus, becomes more dominant compared to the nuclear force attractions, then the nucleus needs more neutrons to gain stability.The presence of more neutrons decrease the density of protons which decreases the repulsion among them.


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A pulley is able to lift a mass of 25 kg 0.30 m with an applied force of 50 N over a distance of 1.5 m. What is the ideal mechan
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The ideal mechanical advantage of the pulley system is 3

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Where do we hear loud sound, at antinode or node?​
tester [92]

Answer:

node

Explanation:

on the graph node is higher than antinode

so it can get or hear loud sounds faster

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3 years ago
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