<span>82.0 kg
I am going to assume that there is a typo for the number of joules of energy. Doing a google search for this exact question showed this question multiple times with a value of 4942 joules which makes sense given how close the "o" key is to the "9" key. Because of this, I will assume that the correct value for the number of joules is 4942. With that in mind, here's the solution.
The gravitational potential energy is expressed as the mass multiplied by the height, multiplied by the local gravitational acceleration. So:
E = MHA
Solving for M, the substituting the known values and calculating gives:
E = MHA
E/(HA) = M
4942/(6.15*9.8) = M
4942/60.27 = M
81.99767712 = M
Rounding to 3 significant figures gives 82.0 kg</span>
Answer:
The value is ![n = 1.527 *10^{14} \ electrons](https://tex.z-dn.net/?f=n%20%20%3D%20%201.527%20%2A10%5E%7B14%7D%20%5C%20%20electrons%20)
Explanation:
From the question we are told that
The mass of the sphere is m = 18.5 kg
The diameter is ![d= 25.0 \ cm = 0.25 \ m](https://tex.z-dn.net/?f=d%3D%2025.0%20%5C%20%20cm%20%20%3D%200.25%20%5C%20%20m)
The number of electrons is ![N = 8.10 *10^{15} \ electrons](https://tex.z-dn.net/?f=N%20%20%3D%20%208.10%20%2A10%5E%7B15%7D%20%5C%20%20electrons)
The mass of the plastic ball is ![m_b = 0.120 g](https://tex.z-dn.net/?f=m_b%20%20%3D%20%200.120%20g)
The initial acceleration of the ball is ![u = 1525\ m/s^2](https://tex.z-dn.net/?f=u%20%3D%201525%5C%20m%2Fs%5E2)
Generally the radius of the sphere is mathematically evaluated as
![r = \frac{d}{2}](https://tex.z-dn.net/?f=r%20%3D%20%20%5Cfrac%7Bd%7D%7B2%7D)
=> ![r = \frac{0.25}{2}](https://tex.z-dn.net/?f=r%20%3D%20%20%5Cfrac%7B0.25%7D%7B2%7D)
=> ![r = 0.125 \ m](https://tex.z-dn.net/?f=r%20%3D%20%200.125%20%5C%20m%20)
Generally the force between the ball and the sphere is
![F = \frac{k * q_1 * q_2 }{r^2}](https://tex.z-dn.net/?f=F%20%3D%20%20%5Cfrac%7Bk%20%2A%20q_1%20%2A%20q_2%20%7D%7Br%5E2%7D)
Generally this force can also be mathematically represented as
![F = m_b * a](https://tex.z-dn.net/?f=F%20%3D%20%20m_b%20%2A%20a)
So
![m_b * a = \frac{k * q_1 * q_2 }{r^2}](https://tex.z-dn.net/?f=%20m_b%20%2A%20a%20%3D%20%20%5Cfrac%7Bk%20%2A%20q_1%20%2A%20q_2%20%7D%7Br%5E2%7D)
Here
is the charge removed from the sphere whicn is evaluated as
![q_1 = N * e](https://tex.z-dn.net/?f=q_1%20%3D%20%20N%20%20%2A%20e)
substituting
for e
![q_1 = 8.10 *10^{15} * 1.60*10^{-19}](https://tex.z-dn.net/?f=q_1%20%3D%20%208.10%20%2A10%5E%7B15%7D%20%20%2A%201.60%2A10%5E%7B-19%7D)
![q_1 = 0.0013 \ C](https://tex.z-dn.net/?f=q_1%20%3D%200.0013%20%5C%20C%20)
and
is the charge to be removed from the ball
So
![0.120 * 1525 = \frac{9*10^9 * 0.0013* q_2 }{0.125^2}](https://tex.z-dn.net/?f=%200.120%20%2A%201525%20%3D%20%20%5Cfrac%7B9%2A10%5E9%20%20%2A%200.0013%2A%20q_2%20%7D%7B0.125%5E2%7D)
![q_2 = 2.44 *10^{-7} \ C](https://tex.z-dn.net/?f=q_2%20%20%3D%20%202.44%20%2A10%5E%7B-7%7D%20%5C%20%20C%20)
Generally the number of electron to be removed from the ball is mathematically represented as
![n = \frac{q_2}{e}](https://tex.z-dn.net/?f=n%20%20%3D%20%20%5Cfrac%7Bq_2%7D%7Be%7D)
=> ![n = \frac{ 2.44 *10^{-7}}{1.60*10^{-19}}](https://tex.z-dn.net/?f=n%20%20%3D%20%20%5Cfrac%7B%202.44%20%2A10%5E%7B-7%7D%7D%7B1.60%2A10%5E%7B-19%7D%7D)
=> ![n = 1.527 *10^{14} \ electrons](https://tex.z-dn.net/?f=n%20%20%3D%20%201.527%20%2A10%5E%7B14%7D%20%5C%20%20electrons%20)
Answer:
3. Work
Explanation:
Number 1 isn't correct because you are not using efficiency to hold books and walk across the room.
Number 2 could be correct but isn't in this situation because you use power only to hold the books but not to walk across the room.
Number 4 is not correct because you need to do work to do something.
Answer:
As a positively charged object moves toward another positively charged object, their potential energy increases. True
As a negatively charged object moves toward another negatively charged object, their potential energy increases True
Explanation:
When two like charges move towards each other, there is increase in potential energy because the motion is in opposition to the direction if the field. Hence when two negative or two positive charges move towards each other, there is an increase in potential energy.
However, potential energy is inversely related to the distance of separation of the charges.
Answer:
1.62 m/s
Explanation:
Wavelength of the water wave= 54 m
The frequency is 0.03 Hz
Therefore the velocity can be calculated as follows
Velocity= frequency × wavelength
= 0.03 × 54
= 1.62 m/s