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Aleks04 [339]
3 years ago
5

A spherical balloon is filled with gas at a rate of 4 cm 3 /s . at what rate is the radius r changing with with respect to time

when the volume v = 36 π cm 3 ?
Physics
1 answer:
Gnoma [55]3 years ago
8 0
The volume of the sphere is given by V = 4/3 * pie * r^3. We seek dr/dt that the rate of change of the radius with respect to time.  
V = 4/3 * pie * r^3 
Since we know the rate at which the volume changes wrt time. We can plug it in to find dr/dt.
 dV/dt = 36pie. But dV/dt = 4/3 * pie * 3r^2 * dr/dt
 So we have that dr/dt = (dV/dt) / 4/3 * pie * 3r^2
 So dr/dt = (36pie)/ 4/3 * pie * 3(4)^2
 dr/dt = 113.112/ 201.0864 = 0.5624

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An object is hung on the end of a vertical spring and is released from rest with the spring 3 unstressed. If the object falls 3.
den301095 [7]

Answer:

The period of the resulting oscillatory motion is 0.20 s.

Explanation:

Given that,

Spring constant k= 3\ N/m^2

We need to calculate the time period

The object is at rest and has no elastic potential but it does has gravitational potential.

If the object falls then the the gravitational potential change in to the elastic potential.

So,

mgh=\dfrac{1}{2}kh^2

m=\dfrac{1}{2}\times\dfrac{kh}{g}

Where,h = distance

k = spring constant

Put the value into the formula

m=\dfrac{1\times3\times3.42\times10^{-2}}{2\times9.8}

m=5.235\times10^{-3}\ kg

Using formula of time period

T=\dfrac{1}{2\pi}\times\sqrt{\dfrac{m}{k}}

Put the value into the formula

T=\dfrac{1}{2\pi}\times\sqrt{\dfrac{5.235\times10^{-2}}{3}}

T=0.20\ sec

Hence, The period of the resulting oscillatory motion is 0.20 s.

8 0
3 years ago
You are given two vectors vector A = 4.9 at 31o vector B = 6 at 156o Angles are measured counterclockwise from the x-axis. What
Ket [755]

Answer:

   C_{y} = 4.96  and     θ' = 104,5º

Explanation:

To add several vectors we can decompose each one of them, perform the sum on each axis, to find the components of the resultant and then find the module and direction.

Let's start by decomposing the two vectors.

Vector A

             sin θ = A_{y} / A

             cos θ = Aₓ / A

             A_{y} = A sin  θ

             Ax = A cos θ

             A_{y} = 4.9 sin 31 = 2.52

             Ax = 4.9 cos 31 = 4.20

Vector B

           B_{y} = B sin θ

           Bx = B cos θ

           B_{y} = 6 sin 156 = 2.44

           Bx = 6 cos 156 = -5.48

The components of the resulting vector are

X axis

         Cx = Ax + B x

         Cx = 4.20 -5.48

         Cx = -1.28

Axis y

         C_{y} = Ay + By

         C_{y} = 2.52 + 2.44  

         C_{y} = 4.96

Let's use the Pythagorean theorem to find modulo

         C = √ (Cₙ²x2 + Cy2)

         C = Ra (1.28 2 + 4.96 2)

         C = 5.12

We use trigonemetry to find the angle

         tan θ = C_{y} / Cₓ

          θ’ = tan⁻¹ (4.96 / (1.28))

           θ’ = 75.5

como el valor de Cy es positivo y Cx es negativo el angulo este en el segundo cuadrante, por lo cual el angulo medido respecto de eje x positivo es

       θ’ = 180 – tes

        θ‘= 180 – 75,5

        θ' = 104,5º

7 0
3 years ago
If two charged objects in a laboratory are brought to a distance of 0.22 meters away from each other. What is
zysi [14]

Answer:

q_2=2.47\times 10^{-4}\ C

Explanation:

The charge on one object, q_1=9.9\times 10^{-5}\ C

The distance between the charges, r = 0.22 m

The force between the charges, F = 4,550 N

Let q₂ is the charge on the other sphere. The electrostatic force between two charges is given by the formula as follows :

F=\dfrac{kq_1q_2}{r^2}\\\\q_2=\dfrac{Fr^2}{kq_1}\\\\q_2=\dfrac{4550\times (0.22) ^2}{9\times 10^9\times 9.9\times 10^{-5}}\\\\q_2=2.47\times 10^{-4}\ C

So, the charge on the other sphere is 2.47\times 10^{-4}\ C.

7 0
3 years ago
How do you know when water is boiling?
vladimir1956 [14]

Answer:

when the steam starts coming out

Explanation:

5 0
3 years ago
Do you think most people follow the recommended guidelines for an adequate exercise routine?
blondinia [14]

Personally, I know that I don't however it all depends on the person's lifestyle, health, and resoucres, such as if they are able to complete the excersise or have enough money fore equpemnt. To be safe, I would say that the majority of people do follow the guidelines although they may manipulate it to fit their best interest.

6 0
3 years ago
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