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Nataliya [291]
3 years ago
11

Two small spheres with mass 10 gm and charge q, are suspended from a point by threads of length L=0.22m. What is the charge on e

ach sphere if the threads make an angle θ of 15 degrees with the vertical?
Physics
1 answer:
Nataliya [291]3 years ago
5 0

Answer:

q=1.95*10^{-7}C

Explanation:

According to the free-body diagram of the system, we have:

\sum F_y: Tcos(15^\circ)-mg=0(1)\\\sum F_x: Tsin(15^\circ)-F_e=0(2)

So, we can solve for T from (1):

T=\frac{mg}{cos(15^\circ)}(3)

Replacing (3) in (2):

(\frac{mg}{cos(15^\circ)})sin(15^\circ)=F_e

The electric force (F_e) is given by the Coulomb's law. Recall that the charge q is the same in both spheres:

(\frac{mg}{cos(15^\circ)})sin(15^\circ)=\frac{kq^2}{r^2}(4)

According to pythagoras theorem, the distance of separation (r) of the spheres are given by:

sin(15^\circ)=\frac{\frac{r}{2}}{L}\\r=2Lsin(15^\circ)(5)

Finally, we replace (5) in (4) and solving for q:

mgtan(15^\circ)=\frac{kq^2}{(2Lsin(15^\circ))^2}\\q=\sqrt{\frac{mgtan(15^\circ)(2Lsin(15^\circ))^2}{k}}\\q=\sqrt{\frac{10*10^{-3}kg(9.8\frac{m}{s^2})tan(15^\circ)(2(0.22m)sin(15^\circ))^2}{8.98*10^{9}\frac{N\cdot m^2}{C^2}}}\\q=1.95*10^{-7}C

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Answer:

f'=5.58kHz

Explanation:

This is an example of the Doppler effect, the formula is:

f'=\frac{(v+v_o)}{(v+v_s)}f

Where f is the actual frequency, f' is the observed frequency, v is the velocity of the sound waves, v_o the velocity of the observer (which is negative if the observer is moving away from the source)  and v_s the velocity of the source  (which is negative if is moving towards the observer). For this problem:

f=3.72kHz\\v=342m/s\\v_o=0m/s\\v_s=-114m/s

f'=\frac{(342+0)}{(342-114)}3.72\times10^3\\f'=\frac{342}{228}3.72\times10^3\\f'=(1.5)3.72\times10^3\\f'=5580Hz=5.58kHz

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What do zooplankton and krill have in common?
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<h2><em>Hello, thank you for choosing brainly today. My name is Ethan and I'll be solving your question. </em><em><u>"What do zooplankton and krill have in common?"</u></em></h2>

Krill and plankton are two groups of organisms found in the ocean. Krill are species of crustacean related to shrimp, and serve as a very important link in the food chain of the sea. Plankton consist of a larger group of organisms with much more variety, including bacteria, algae, protozoans, jellyfish and some species of cephalopods.

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A mass of 5kg starts from rest and pulls down vertically on a string wound around a disk-shaped, massive pulley. The mass of the
Paha777 [63]

Answer:

c. V = 2 m/s

Explanation:

Using the conservation of energy:

E_i =E_f

so:

Mgh = \frac{1}{2}IW^2 +\frac{1}{2}MV^2

where M is the mass, g the gravity, h the altitude, I the moment of inertia of the pulley, W the angular velocity of the pulley and V the velocity of the mass.

Also we know that:

V = WR

Where R is the radius of the disk, so:

W = V/R

Also, the moment of inertia of the disk is equal to:

I = \frac{1}{2}MR^2

I = \frac{1}{2}(5kg)(2m)^2

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so, we can write the initial equation as:

Mgh = \frac{1}{2}IV^2/R^2 +\frac{1}{2}MV^2

Replacing the data:

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solving for V:

(5kg)(9.8)(0.3m) = V^2(\frac{1}{2}(10)1/4 +\frac{1}{2}(5kg))

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