An aeroplane flew at 600mph for 7 hours. How far did it travel?

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

3 years ago

Which list of properties of alternation current is the most likely reason it was chosen over direct current to provide electrici

Paraphin [41]

Answer:

- Direct current is a current in which electrons flow in one direction only

- Alternating current is a current in which the direction of the electron flow reverses periodically - so, half a cycle forward, half a cycle backward

There are several advantages of using alternating currents for the transmission of electricity across a country, over large distances. The main advantages are:

- The voltage of alternating currents can be easily increased/decreased by using transformers. For instance, a transformer is used at the beginning of the transmission line to increase the voltage (electricity is transmitted at high voltage in order to reduce dissipated power), and then another transformer is used before the electricity enters the houses, in order to decrease the voltage. Transformers only work with alternating currents.

- It is easy to interrupt the flow of an alternating current, because its value naturally becomes zero every half a cycle, so this is useful in case the current must be interrupted.

8 0

3 years ago

A constant net torque is exerted on an object. Which of the following quantities for the object cannot be constant? (Select all

prohojiy [21]

Answer:

A. kinetic energy

B. angular velocity

E. angular position

Explanation:

The quantities that cannot be constant if a constant net torque is exerted on an objecta are:

A. Kinetic energy. If a torque is applied, the linear or angular speed will be changing at a rate proportional to the torque, so the kinetic energy will change too.

B. Angular velocity. It will change at a rate equal to the torque.

C. Angular position. If the angular velocity changes, the angular position will change.

3 0

3 years ago

A 142 kg boulder is located near the edge of a cliff 25 m above the ground. What is the gravitational potential energy of the bo

jarptica [38.1K]

PE = mass * height * 9.81
PE = 142 * 25 * 9.81
PE = 34825.5 J

8 0

3 years ago

Read 2 more answers

Charina says that when waves interact with an object, they will interfere with the object, and when waves interact with other wa

Fofino [41]

I would not agree with her since reflection and refraction happens only when waves hit an object. When, waves meet it is either it experiences constructive or destructive interference. Hope this answers the question. Have a nice day.

3 0

3 years ago

Read 2 more answers