Changing the length of an air column will alter its _______
2 answers:
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5) Due to the conservation of energy / due to the presence of friction
6) The work done is 4000 J
7) The distance travelled by the object is 4 m
8) The potential energy of the bird is 2450 J
Explanation:
5)
For a roller coaster in motion along the track, in absence of friction, the mechanical energy remains constant:
where
U is the potential energy
K is the kinetic energy
At the beginning, the roller coaster is at rest, therefore its kinetic energy is zero and its mechanical energy is just equal to the potential energy:
where m is the mass of the roller coaster, g the acceleration of gravity, and h the height of the roller coaster above the ground at the first hill.
Since this amount of energy remains constant, the roller coaster cannot go to a higher hill: in fact, in that case it would reach a height , but this is not possible, because it would mean that its mechanical energy would be
, larger than its mechanical energy, and since energy cannot be created (law of conservation of energy), the height of the next hills cannot be higher than the first one. Moreover, if we consider friction, then friction does work on the roller coaster in motion, and as a result, part of its mechanical energy is wasted (converted into thermal energy): therefore, the height of the following hills must be lower than the height of the first hill.
6)
The work done when lifting an object is equal to the gravitational potential energy gained by the object:
where
F is the weight of the object
h is the change in height of the object
For the object in this problem, we have
F = 200 N (weight)
h = 20 m (change in height)
Substituting, we find the work done:
7)
The work done when pushing an object in a direction parallel to the motion of the object is given by:
where
F is the magnitude of the force
d is the distance through which the object has travelled through
In this problem, we have:
W = 300 J (work done)
F = 75 N (magnitude of the force)
Solving the equation for d, we find the distance travelled:
8)
The potential energy of an object is the energy possessed by an object due to its position in a gravitational field. Near the Earth's surface, it is given by
where
m is the mass of the object
g is the acceleration of gravity
h is the height of the object relative to the ground
For the bird in this problem, we have:
m = 5 kg (mass)
h = 50 m (height)
Substituting, we find:
Learn more about potential energy:
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We can find the answer step-by-step:
1) The electric charges on a conductor must lie entirely on its surface. This is because the charges have same sign, so the force acting between each other is repulsive therefore the charges must be as far apart as possible, i.e. on the surface of the conductor.
2) We consider a cylinder perpendicular to the surface of the conductor, that crosses the surface with its section. We then apply Gauss law, which states that the flux of the electric field through this cylinder is equal to the total charge inside it divided the electrical permittivity:
3) The electric field outside the surface is perpendicular to the surface itself (otherwise there would be a component of the electric force parallel to the surface, which would move the charge, violating the condition of equilibrium). The electric field inside the conductor is instead zero, because otherwise charges would move violating again equilibrium condition. Therefore, the only flux is the one crossing the section A of the cylinder outside the surface:
4) The total charge contained in the cylinder is the product between the section, A, and the charge density
on the surface of the conductor:
5) Substituting the flux and the charge density inside Gauss law, we can find the electric field just outside the surface of the conductor:
therefore
1) The electric charges on a conductor must lie entirely on its surface. This is because the charges have same sign, so the force acting between each other is repulsive therefore the charges must be as far apart as possible, i.e. on the surface of the conductor.
2) We consider a cylinder perpendicular to the surface of the conductor, that crosses the surface with its section. We then apply Gauss law, which states that the flux of the electric field through this cylinder is equal to the total charge inside it divided the electrical permittivity:
3) The electric field outside the surface is perpendicular to the surface itself (otherwise there would be a component of the electric force parallel to the surface, which would move the charge, violating the condition of equilibrium). The electric field inside the conductor is instead zero, because otherwise charges would move violating again equilibrium condition. Therefore, the only flux is the one crossing the section A of the cylinder outside the surface:
4) The total charge contained in the cylinder is the product between the section, A, and the charge density
5) Substituting the flux and the charge density inside Gauss law, we can find the electric field just outside the surface of the conductor:
therefore