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4 years ago

How do you get: a = -ω^2x from: a = -Aω^2sen(ωt) ?

Physics

1 answer:

Firdavs [7]4 years ago

8 0

Answer:

$x = Asin(\omega t)\\v = \frac{dx}{dt} = \omega Acos(\omega t)\\a = \frac{dv}{dt} = -\omega^2Asin(\omega t)= -\omega^2x$

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A parallel-plate capacitor with plates of area 360 cm2 is charged to a potential difference V and is then disconnected from the

Softa [21]

Answer:

$Q=3.9825\times 10^{-9} C$

Explanation:

We are given that a parallel- plate capacitor is charged to a potential difference V and then disconnected from the voltage source.

1 m =100 cm

Surface area =S= $\frac{360}{10000}=0.036 m^2$

$\Delta d=0.8 cm=0.008 m$

$\Delta V=100 V$

We have to find the charge Q on the positive plates of the capacitor.

V=Initial voltage between plates

d=Initial distance between plates

Initial Capacitance of capacitor

$C=\frac{\epsilon_0 S}{d}$

Capacitance of capacitor after moving plates

$C_1=\frac{\epsilon_0 S}{(d+\Delta d)}$

$V=\frac{Q}{C}$

Potential difference between plates after moving

$V=\frac{Q}{C_1}$

$V+\Delta V=\frac{Q}{C_1}$

$\frac{Qd}{\epsilon_0S}+100=\frac{Q(d+\Delta d)}{\epsilon_0S}$

$\frac{Q(d+\Delta d)}{\epsilon_0 S}-\frac{Qd}{\epsilon_0S}=100$

$\frac{Q\Delta d}{\epsilon_0 S}=100$

$\epsilon_0=8.85\times 10^{-12}$

$Q=\frac{100\times 8.85\times 10^{-12}\times 0.036}{0.008}$

$Q=3.9825\times 10^{-9} C$

Hence, the charge on positive plate of capacitor= $Q=3.9825\times 10^{-9} C$

6 0

4 years ago

A 12000 kg train engine moving at 2.2 m/s hits and locks into 3 boxcars with a total mass of 25000 kg sitting still. If the coll

PilotLPTM [1.2K]

Answer:

V = 0.714m/s

Explanation:

Full solution calculation can be found in the attachment below.

From the principle of conservation of linear momentum, the sum of momentum before collision equals the sum of momentum after collision.

Before collision only the train had momentum. After the collision the train and the boxcars stick together and move as one body. The initial momentum of the train is now shared with the boxcars as they move together as one body. The both move with a common velocity v.

See the attachment below for the solution calculation.

5 0

3 years ago

Read 2 more answers

The breaking car had 10,000 J of kinetic energy before breaking after breaking it had 2000 J of kinetic energy. How much thermal

WINSTONCH [101]

Answer:

8000J

Explanation:

The kinetic energy of the car lost during breaking are converted to thermal energy and are gained by the brakes.

Kinetic energy loss by car = thermal energy gained by brakes.

∆K.E = ∆T.E ....1

The Kinetic energy loss by car can be expressed as;

∆K.E = K.E1 - K.E2

Initial K.E = K.E1 = 10000J

Final K.E = K.E2 = 2000J

∆K.E= 10000J - 2000J = 8000J

From equation 1,

∆K.E = ∆T.E

∆T.E = 8,000J

thermal energy gain by brakes = 8,000J

8 0

3 years ago

An arrow is launched from a bow with an initial horizontal velocity of 40

Ivan

Answer:

V = (Vx^2 + Vy^2)^1/2 = (40^2 + 62^2)^1/2

V = 73.8 m/s

tan theta = Vy / Vx = 62/40 = 1.55

theta = 57.2 deg

4 0

3 years ago

A rock falls from a tower that is 320 feet high. As it is falling, its height is given by the formula h equals 320 minus 16 t s

RSB [31]

Answer:

a. 4.5secs

Explanation:

From the question, the equation describing the height is given by

$h(t)=320-16t^{2}\\$

at the point when the rock hit the ground, the height,h will be zero.

Hence we can have

$h(t)=320-16t^{2}\\\\at h(t)=0\\0=320-16t^{2}\\hence \\320=16t^{2}\\t^{2}=\frac{320}{16}\\ t^{2}=20\\t=\sqrt{20}\\ t=4.47secs\\t=4.5sec\\$

hence the rock will hit the ground in 4.5secs

4 0

4 years ago

How do you get: a = -ω^2*x from: a = -Aω^2*sen(ωt) ?

How do you get: a = -ω^2x from: a = -Aω^2sen(ωt) ?