Energy is dissipated from a rollercoaster cart as it mo es along the track.

Two identical small metal spheres with q1 > 0 and |q1| > |q2| attract each other with a force of magnitude 72.1 mN when se

Brrunno [24]

1) $+2.19\mu C$

The electrostatic force between two charges is given by

$F=k\frac{q_1 q_2}{r^2}$ (1)

where

k is the Coulomb's constant

q1, q2 are the two charges

r is the separation between the charges

When the two spheres are brought in contact with each other, the charge equally redistribute among the two spheres, such that each sphere will have a charge of

$\frac{Q}{2}$

where Q is the total charge between the two spheres.

So we can actually rewrite the force as

$F=k\frac{(\frac{Q}{2})^2}{r^2}$

And since we know that

r = 1.41 m (distance between the spheres)

$F= 21.63 mN = 0.02163 N$

(the sign is positive since the charges repel each other)

We can solve the equation for Q:

$Q=2\sqrt{\frac{Fr^2}{k}}=2\sqrt{\frac{(0.02163)(1.41)^2}{8.98755\cdot 10^9}}}=4.37\cdot 10^{-6} C$

So, the final charge on the sphere on the right is

$\frac{Q}{2}=\frac{4.37\cdot 10^{-6} C}{2}=2.19\cdot 10^{-6}C=+2.19\mu C$

2) $q_1 = +6.70 \mu C$

Now we know the total charge initially on the two spheres. Moreover, at the beginning we know that

$F = -72.1 mN = -0.0721 N$ (we put a negative sign since the force is attractive, which means that the charges have opposite signs)

r = 1.41 m is the separation between the charges

And also,

$q_2 = Q-q_1$

So we can rewrite eq.(1) as

$F=k \frac{q_1 (Q-q_1)}{r^2}$

Solving for q1,

$Fr^2=k (q_1 Q-q_1^2})\\kq_1^2 -kQ q_1 +Fr^2 = 0$

Since $Q=4.37\cdot 10^{-6} C$ , we can substituting all numbers into the equation:

$8.98755\cdot 10^9 q_1^2 -3.93\cdot 10^4 q_1 -0.141 = 0$

which gives two solutions:

$q_1 = 6.70\cdot 10^{-6} C\\q_2 = -2.34\cdot 10^{-6} C$

Which correspond to the values of the two charges. Therefore, the initial charge q1 on the first sphere is

$q_1 = +6.70 \mu C$

8 0

4 years ago

Present the ways to observe interference patterns on thin films. Why the thickness of thin films should be in scale of wavelengt

antoniya [11.8K]

Answer:

A colorful interference pattern is observed when light is reflected from the top and bottom boundaries of a thin oil film. The different bands form as the film's thickness diminishes from a central run-off-poin

Explanation:

<h3>hope it help brainliest pls</h3>

5 0

3 years ago

Read 2 more answers

What is the density of an object with a mass of 60g and a volume of 2cm3?

zaharov [31]

m= 60g = 60/1000 Kg = 0.06 Kg v = 2cm3 = 2 * (0.01^3) m3 = 2 *10^-6 m3 Density= m/v = 6 * 10^-2 / 2 *10^-6 = 3 *10^4 Kg/m3

8 0

3 years ago

Please Help Me!!!.........

Effectus [21]

C look at how many oxygen, nitrogen’s, and hydrogens there are

8 0

3 years ago

Read 2 more answers

How are these ions distinguished from one another in writing formulas for compounds? A. using Latin prefixes B. using numerical

IgorC [24]

Answer:

B. using numerical superscripts

Explanation:

ion is an atom that has different number of protons and electrons. An isotope is an atom of an element with a specific number of neutrons. Two different isotopes of the same element will have two different neutron counts.

When writing the symbol for an ion, the one- or two-letter element symbol is written first, followed by a superscript. The superscript has the number of charges on the ion followed by a + (for positive ions or cations) or - (for negative ions or anions). Neutral atoms have a charge of zero, so no superscript is given.

5 0

3 years ago