1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
lidiya [134]
3 years ago
12

Use the information below to answer questions

Physics
1 answer:
Ulleksa [173]3 years ago
5 0

Answer:

The charges are q₁  = 2 × 10⁻⁸ C and  q₂ = 3 × 10⁻⁸ C

Explanation:

Here is the complete question

Two identical tiny balls have charge q1 and q2. The repulsive force one exerts on the other when they are 20cm apart is 1.35 X 10-4 N. after the balls are touched together and then represented once again to 20cm, now the repulsive force is found to be 1.40 X 10-4 N. find the charges q1 and q2.

Solution

The force F = 1.35 × 10⁻⁴ N when the charges are separated a distance of r = 20 cm = 0.2 m is given by

F = kq₁q₂/r₁²

q₁q₂ = Fr₁²/k

q₁q₂ = 1.35 × 10⁻⁴ N × (0.2 m)²/9 × 10⁹ Nm²/C² = 0.054/9 × 10⁻¹³ C² = 0.006 × 10⁻¹³ C² = 6 × 10⁻¹⁶ C²

q₁q₂ = 6 × 10⁻¹⁶ C² (1)

When the charges are brought together, the charge is now q = (q₁ + q₂)/2

The new repulsive force F = 1.406 × 10⁻⁴ N  at a distance of r₂ = 20 cm = 0.2 m is then

F₂ = kq²/r₂²

q² = F₂r₂²/k = 1.406 × 10⁻⁴ N × (0.2 m)²/9 × 10⁹ Nm²/C² = 0.00625 × 10⁻¹³ C² = 6.25 × 10⁻¹⁶ C²

q² = 6.25 × 10⁻¹⁶ C²

q = √(6.25 × 10⁻¹⁶) C

q = 2.5 × 10⁻⁸ C

(q₁ + q₂)/2 =  2.5 × 10⁻⁸ C

(q₁ + q₂) = 2 × 2.5 × 10⁻⁸ C

q₁ + q₂ = 5 × 10⁻⁸ C (2)

q₁  = 5 × 10⁻⁸ C - q₂  (3)

Substituting equation (3) into (1), we have

(5 × 10⁻⁸ C - q₂)q₂ = 6 × 10⁻¹⁶ C²

Expanding the bracket, we have

(5 × 10⁻⁸ C)q₂ - q₂² = 6 × 10⁻¹⁶ C²

So, q₂² - (5 × 10⁻⁸ C)q₂ + 6 × 10⁻¹⁶ C² = 0

Using the quadratic formula to find q₂

q_{2} = \frac{-(-5 X 10^{-8} )+/- \sqrt{(-5 X 10^{-8} )^{2} - 4X1X6 X 10^{-16} } }{2X1}\\  = \frac{5 X 10^{-8} )+/- \sqrt{25 X 10^{-16}  - 24 X 10^{-16} } }{2}\\= \frac{5 X 10^{-8} )+/- \sqrt{1 X 10^{-16} } }{2}\\= \frac{5 X 10^{-8} )+/- 1 X 10^{-8} }{2}\\= \frac{5 X 10^{-8} + 1 X 10^{-8} }{2} or \frac{5 X 10^{-8}  - 1 X 10^{-8} }{2}\\= \frac{6 X 10^{-8} }{2} or \frac{4 X 10^{-8}}{2}\\= 3 X 10^{-8} C or 2 X 10^{-8} C

q₁  = 5 × 10⁻⁸ C - q₂

q₁  = 5 × 10⁻⁸ C - 3 × 10⁻⁸ C or 5 × 10⁻⁸ C - 2 × 10⁻⁸ C

q₁  = 2 × 10⁻⁸ C or 3 × 10⁻⁸ C

So the charges are q₁  = 2 × 10⁻⁸ C and  q₂ = 3 × 10⁻⁸ C

You might be interested in
An object moves on a trajectory given by Bold r left parenthesis t right parenthesis equals left angle 10 cosine 6 t comma 10 si
spayn [35]

Answer:

10

Explanation:

(r) = <10 cos 6t, 10 Sin 6t>

The distance traveled by the object is the magnitude of vector r.

The magnitude of vector r is given by

r = \sqrt{(10 Cos 6t)^{2}+(10 Sin 6t)^{2}}

r =10 \sqrt{(Cos^{2} 6t)+(Sin^{2} 6t)

r = 10        

5 0
3 years ago
A spelunker is surveying a cave. She follows a passage 140 m straight west, then 290 m in a direction 45? east of south, and the
zimovet [89]

Answer:

Magnitude of fourth displacement is approximately 95 metres,

Direction of fourth displacement is straight west.

3 0
3 years ago
Sandra takes a class field trip to a geology museum. She sees an interesting sample of igneous rock. She wonders if the material
Aleonysh [2.5K]

Answer:

Yes

Explanation:

It is possible for sedimentary rocks to be converted to igneous rocks. Under conditions of high temperature and pressure, sedimentary rocks can be broken down into igneous rock by melting this rock type.

When the rock is broken down, it forms melt which when cooled and solidifies will form igneous rocks.

Sedimentary rocks are formed from the breaking down of pre-existing rocks through the action of weathering, erosion and sediment transportation. Within a basin, the sediments are compacted and lithified.

When this is subjected to intense pressure and temperature, the rock hardens and might further break down to melt.

6 0
3 years ago
Sound source A has a deciBel rating of 50 dB. Sound source B is 1000 times more intense. What is the deciBel rating of B
masha68 [24]

The decibel system of sound intensity operates by a logarithmic scale, meaning that sound intensity increases exponentially in relation to the decibel rating.

For decibels, the equation between intensity and the dB equivalent is:

dB = 10log(i),

where “i” is the intensity of the sound. The ten in front of the log means that an increase in ten dB results in a tenfold increase in sound intensity; for example, a 30 dB sound is ten times softer than a 40 dB sound.

In this case, a sound with a dB of 80 would be 1000 times more intense than a 50 dB sound, so the decibel rating of B is 80.

Hope this helps!

3 0
3 years ago
In the nuclear fission process mass is converted into energy. Determine the total mass that must be converted to energy in one y
brilliants [131]

Answer:

1) Mass that needs to be converted at 100% efficiency is 0.3504 kg

2) Mass that needs to be converted at 30% efficiency is 1.168 kg

Explanation:

By the principle of mass energy equivalence we have

E=mc^{2}

where,

'E' is the energy produced

'm' is the mass consumed

'c' is the velocity of light in free space

Now the energy produced by the reactor in 1 year equals

Energy=Power\times time\\\\\therefore Energy=1\times 10^{9}\times 365\times 24\times 3600\\\\Energy=31.536\times 10^{15}Joules

Thus the mass that is covertred at 100% efficiency is

mass=\frac{Energy}{c^{2}}\\\\mass=\frac{31.536\times 10^{15}}{(3\times 10^{8})^{2}}\\\\mass=\frac{31.536\times 10^{15}}{9\times 10^{16}}\\\\\therefore mass=0.3504kg

Part 2)

At 30% efficiency the mass converted equals

mass|_{30}=\frac{mass|_{100}}{0.3}\\\\mass|_{30}=\frac{0.3504}{0.3}\\\\mass|_{30}=1.168kg

8 0
3 years ago
Other questions:
  • You are riding on your bike and stop pedaling , coasting along the road. eventually, your bike slows down and stops. what happen
    12·1 answer
  • Isabela is an astronomer studying stars A and B. Star A is farther away from Isabela and yet when Isabela observes the stars, th
    13·1 answer
  • a fisherman hooks a trout and reels in his line at speed of 4 inches/second. assume tip of fishing rod is 12 ft above the water
    13·2 answers
  • What do lines on a contour map indicate
    7·1 answer
  • Why don't ring particles form a moon? a. They collide too violently to accrete into a moon. b. Tidal forces from moons prevent t
    14·1 answer
  • The critical angle for a substance is measured at 53.7 degrees. Light enters from air at 45.0 degrees. At what angle it will con
    13·1 answer
  • 5. Atoms may emit light energy when
    7·1 answer
  • What kind of energy transformations occur when you hit a coconut with a hammer?
    7·1 answer
  • A heat turbine can generate a maximum power of 250 MW. How much work can the turbine do in
    15·1 answer
  • If you do 40 j of work in 4s, how much power did you generate?
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!