What is universal laws of gravitation
1 answer:
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Answer:
The spring force constant is .
Explanation:
We are told the mass of the ball is , the height above the spring where the ball is dropped is
, the length the ball compresses the spring is
and the acceleration of gravity is
.
We will consider the initial moment to be when the ball is dropped and the final moment to be when the ball stops, compressing the spring. We supose that there is no friction so the initial mechanical energy is equal to the final mechanical energy
:
Initially there is only gravitational potential energy because the force of the spring isn't present and the speed is zero. In the final moment there is only elastic potential energy because the height is zero and the ball has stopped. So we have that:
If we manipulate the equation we have that:
Answer:
See explanation
Explanation:
Solution:-
Electric current produces a magnetic field. This magnetic field can be visualized as a pattern of circular field lines surrounding a wire. One way to explore the direction of a magnetic field is with a compass, as shown by a long straight current-carrying wire in. Hall probes can determine the magnitude of the field. Another version of the right hand rule emerges from this exploration and is valid for any current segment—point the thumb in the direction of the current, and the fingers curl in the direction of the magnetic field loops created by it.
Compasses placed near a long straight current-carrying wire indicate that field lines form circular loops centered on the wire. Right hand rule 2 states that, if the right hand thumb points in the direction of the current, the fingers curl in the direction of the field. This rule is consistent with the field mapped for the long straight wire and is valid for any current segment.
( See attachments )
- The equation for the magnetic field strength - B - (magnitude) produced by a long straight current-carrying wire is given by the Biot Savart Law:
Where,
I : The current,
r : The shortest distance to the wire,
uo : The permeability of free space. = 4π * 10^-7 T. m/A
- Since the wire is very long, the magnitude of the field depends only on distance from the wire r, not on position along the wire. This is one of the simplest cases to calculate the magnetic field strength - B - from a current.
- The magnetic field of a long straight wire has more implications than one might first suspect. Each segment of current produces a magnetic field like that of a long straight wire, and the total field of any shape current is the vector sum of the fields due to each segment. The formal statement of the direction and magnitude of the field due to each segment is called the Biot-Savart law. Integral calculus is needed to sum the field for an arbitrary shape current. The Biot-Savart law is written in its complete form as:
Where the integral sums over,
1) The wire length where vector dl = direction of current (in or out of plane)
2) r is the distance between the location of dl and the location at which the magnetic field is being calculated
3) r^ is a unit vector in the direction of r.
The change in kinetic energy is
Explanation:
According to the work-energy theorem, the work done on an object is equal to the change in kinetic energy of the object. Mathematically:
where :
W is the work done on the object
is the final kinetic energy of the object
is the initial kinetic energy
Also, the work done on an object is (assuming that the force is applied parallel to the motion of the object):
where
F is the magnitude of the force
is the displacement of the object
In this problem, the force acting on the object is
F
While the displacement is the horizontal distance travelled, so
Therefore, the work done is
And so the change in kinetic energy is
Learn more about work and kinetic energy:
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