Answer:
All three pendulums will have the same angular frequencies.
Explanation:
For a simple pendulum, the time period using the approximation 
is expressed as:
The angular frequency 
is defined as
Since the angular frequency remains unaffected by the initial angle (valid strictly for small angle approximations), we deduce that the angular frequencies of the three pendulums are identical.
Answer:
1.43 x 10¹⁷.
They will move away from each other.
Explanation:
The force acting on each charged sphere is determined as F = mass x acceleration
= 8.55 x 10⁻³ x 25 x 9.8
= 2.095 N
Assuming Q is the charge on each sphere
F = 
Using the values, 2.095 =
We find that Q² = 
Thus, Q = 2.289 X 10⁻⁶
The quantity of electrons = Charge / charge of a single electron
= 
=1.43 x 10¹³.
They will accelerate away from each other.
Answer:
Explanation:
For a 60W light bulb used for 1 minute:
P = 60 W
t = 1 minute = 60 seconds
This energy is capable of lifting an object weighing 10N.
W = 10N
This indicates conversion of electrical energy into potential energy.
Let's calculate the electrical energy:
Power describes the rate of work done.
Power = Work / time
Thus, work = power × time
Work = 60 × 60
Work = 3600 J
Potential energy calculation:
P.E = mgh
Where the weight is given by:
W = mg
Therefore, P.E = W·h
P.E = 10·h
Thus, we equate:
Potential energy = Electrical energy
P.E = Work
10·h = 3600
Dividing both sides by 10 gives:
h = 3600 / 10
h = 360m
The object can be lifted to a height of 360m.
Since the absolute values of the charges are identical, the changes in potential energy remain equivalent. Consequently, the changes in kinetic energy will also match. We have:
1 = Ke/Kp = m_e * v_e^2 / m_p * v_p^2, which simplifies to:
v_e/v_p = sqrt(m_p/m_e),
indicating that the velocity of the electron is sqrt(m_p/m_e) times greater than that of the proton.
Answer:
Please refer to the explanation
Explanation:
Race distance is 5km
Top speed = 45 yards
Converting yards to kilometers:
1km equals 1093.613 yards
x = 45 yards
(1093.613 * x) = 45
x = 45 / 1093.613
x = 0.0411480 km
Where x indicates the maximum distance he can sustain his highest speed in kilometers.
Thus, from the data available, we can determine that Lamar will not be able to maintain his maximum speed for the full 5km race, as he can only sustain it for 0.0411 kilometers.
