The total mechanical energy of the system at any time t is the sum of the kinetic energy of motion of the ball and the elastic potential energy stored in the spring:

where m is the mass of the ball, v its speed, k the spring constant and x the displacement of the spring with respect its rest position.
Since it is a harmonic motion, kinetic energy is continuously converted into elastic potential energy and vice-versa.
When the spring is at its maximum displacement, the elastic potential energy is maximum (because the displacement x is maximum) while the kinetic energy is zero (because the velocity of the ball is zero), so in this situation we have:

Instead, when the spring crosses its rest position, the elastic potential energy is zero (because x=0) and therefore the kinetic energy is at maximum (and so, the ball is at its maximum speed):

Since the total energy E is always conserved, the maximum elastic potential energy should be equal to the maximum kinetic energy, and so we can find the value of the maximum speed of the ball:


In physics, displacement is a physical quantity that is used to describe the overall change in the position of an object/person.
In other words, it describes how far you are from your initial position.
In the given problem, the initial position is the same as the final position. This means that overall change in position is zero, which also means that the difference between the final and initial positions is zero.
Based on the above, the displacement is zero.
The De Broglie's wavelength of a particle is given by:

where
is the Planck constant
p is the momentum of the particle
In this problem, the momentum of the electron is equal to the product between its mass and its speed:

and if we substitute this into the previous equation, we find the De Broglie wavelength of the electron:

So, the answer is True.
Given,
The initial inside diameter of the pipe, d₁=4.50 cm=0.045 m
The initial speed of the water, v₁=12.5 m/s
The diameter of the pipe at a later position, d₂=6.25 cm=0.065 m
From the continuity equation,

Where A₁ is the area of the cross-section at the initial position, A₂ is the area of the cross-section of the pipe at a later position, and v₂ is the flow rate of the water at the later position.
On substituting the known values,

Thus, the flow rate of the water at the later position is 5.99 m/s
Answer:
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Explanation: