The image shows a pendulum that is released from rest at point A. Shari tells her friend that no energy transformation occurs as
the pendulum swings between point B and point D.
What is the best response that Shari’s friend could make?
She could agree with Shari because the pendulum is at the same height and would have the same gravitational potential energy at both positions.
She could agree with Shari because the pendulum has the same amount of mechanical energy throughout its swing.
She could disagree with Shari because the pendulum converts kinetic energy into gravitational potential energy, then back into kinetic energy.
She could disagree with Shari because the pendulum converts gravitational potential energy into kinetic energy, then back into gravitational potential energy.
What is the best response that Shari’s friend could make?
She could agree with Shari because the pendulum is at the same height and would have the same gravitational potential energy at both positions.
She could agree with Shari because the pendulum has the same amount of mechanical energy throughout its swing.
She could disagree with Shari because the pendulum converts kinetic energy into gravitational potential energy, then back into kinetic energy.
She could disagree with Shari because the pendulum converts gravitational potential energy into kinetic energy, then back into gravitational potential energy.
2 answers:
Answer:
She could disagree with Shari because the pendulum converts gravitational potential energy into kinetic energy, then back into gravitational potential energy.
Explanation:
The energy of the pendulum is constantly converted from gravitational potential to kinetic, and back.
In fact:
- the gravitational potential energy of the pendulum is given by:
where m is the mass of the pendulum, g is the gravitational acceleration, and h is the height of the pendulum above the ground
- The kinetic energy of the pendulum is given by:
where v is the speed of the pendulum.
Therefore, when it is at a higher position, the pendulum has a greater potential energy, while when it is at a lower position, the pendulum has a greater kinetic energy (because its speed is higher).
In this example:
- when the pendulum swings from B to C, part of its gravitational potential energy is converted into kinetic energy (because the height decreases but the speed increases), and when the pendulum goes from C to D, the kinetic energy is converted back into gravitational potential energy (because the height increases and the speed decreases)
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Answer:
For the point inside the cylinder:
For the point outside the cylinder:
where x0 is the position of the point on the x-axis and σ is the surface charge density.
Explanation:
Let us assume that the finite end of the cylinder is positioned at the origin. And the rest of the cylinder lies on the (-x) axis, which is the vertical axis in this question. In the first case (inside the cylinder) we will calculate the electric field at an arbitrary point -x0. In the second case (outside), the point will be +x0.
<u>x = -x0:</u>
The cylinder is consist of the sum of the rings with the same radius.
First we will calculate the electric field at point -x0 created by the ring at an arbitrary point x.
We will also separate the ring into infinitesimal portions of length 'ds' where ds = Rdθ.
The charge of the portion 'ds' is 'dq' where dq = σds = σRdθ. σ is the surface charge density.
Now, the electric field created by the small portion is 'dE'.
The electric field is a vector, and it needs to be separated into its components in order us to integrate it. But, the sum of horizontal components is zero due to symmetry. Every dE has an equal but opposite counterpart which cancels it out. So, we only need to take the component with the sine term.
We have to integrate it over the ring, which is an angular integration.
This is the electric field created by a ring a distance x away from the point -x0. Now we can integrate this electric field over the semi-infinite cylinder to find the total E-field:
The reason we integrate over -2x0 to -inf is that the rings above -x0 and below to-2x0 cancel out each other. Electric field is created by the rings below -2x0 to -inf.
<u>x = +x0: </u>
We will only change the boundaries of the last integration.
the electric force decreases because the distance has an indirect relationship to the force
Explanation:
The electric force between two objects is given by
where
k is the Coulomb's constant
q1 and q2 are the charges of the two objects
r is the distance between the two objects
As we can see from the formula, the magnitude of the force is inversely proportional to the square of the distance: so, when the distance between the object increases, the magnitude of the force decreases.