The total amount of potential and kinetic energy in an object is called mechanical energy. True or False
1 answer:
True: The mechanical energy is the sum of the kinetic energy and the potential energy of a body
Explanation:
The mechanical energy of a body is the sum of its kinetic energy and its potential energy:
E = K + U
where
K is the kinetic energy
U is the potential energy
The kinetic energy of a body is the energy possessed by a body due to its motion, and it is given by
where
m is the mass of the body
v is its speed
The potential energy of a body can have different forms; the most common one is the gravitational potential energy (GPE), which is the energy possessed by a body due to its position in a gravitational field. Near the Earth's surface, it can be calculated as
where
m is the mass of the body
g is the acceleration of gravity
h is the height of the object above the ground
When there are no frictional forces acting on a system, the total mechanical energy of a body is conserved. An example of this is a body in free fall: as the body falls down, the gravitational potential energy is converted into kinetic energy (because the height h decreases, while the speed v increases), however the total mechanical energy, E, remains constant.
Learn more about kinetic energy and potential energy:
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a)
(+x axis)
b)
(+x axis)
(+z axis)
c)
(+x axis)
(+y axis)
(-x axis)
Explanation:
a)
The electric force exerted on a charged particle is given by
where
q is the charge
E is the electric field
For a positive charge, the direction of the force is the same as the electric field.
In this problem:
is the charge
is the electric field, along the x-direction
So the electric force (along the x-direction) is:
towards positive x-direction.
The magnetic force instead is given by
where
q is the charge
v is the velocity of the charge
B is the magnetic field
is the angle between the directions of v and B
Here the charge is stationary: this means , therefore the magnetic force due to each component of the magnetic field is zero.
b)
In this case, the particle is moving along the +x axis.
The magnitude of the electric force does not depend on the speed: therefore, the electric force on the particle here is the same as in part a,
(towards positive x-direction)
Concerning the magnetic force, we have to analyze the two different fields:
- : this field is parallel to the velocity of the particle, which is moving along the +x axis. Therefore,
, so the force due to this field is zero.
: this field is perpendicular to the velocity of the particle, which is moving along the +x axis. Therefore,
. Therefore,
, so the force due to this field is:
where:
is the charge
is the velocity
is the magnetic field
Substituting,
And the direction of this force can be found using the right-hand rule:
- Index finger: direction of the velocity (+x axis)
- Middle finger: direction of the magnetic field (+y axis)
- Thumb: direction of the force (+z axis)
c)
As in part b), the electric force has not change, since it does not depend on the veocity of the particle:
(+x axis)
For the field , the velocity (+z axis) is now perpendicular to the magnetic field (+x axis), so the force is
And by substituting,
And by using the right-hand rule:
- Index finger: velocity (+z axis)
- Middle finger: magnetic field (+x axis)
- Thumb: force (+y axis)
For the field , the velocity (+z axis) is also perpendicular to the magnetic field (+y axis), so the force is
And by substituting,
And by using the right-hand rule:
- Index finger: velocity (+z axis)
- Middle finger: magnetic field (+y axis)
- Thumb: force (-y axis)