In a science museum, a 140 kg brass pendulum bob swings at the end of a 16.8 m -long wire.
1 answer:
The period of the pendulum is 8.2 s
Explanation:
The period of a simple pendulum is given by the equation:
where
L is the length of the pendulum
g is the acceleration of gravity
T is the period
We notice that the period of a pendulum does not depend at all on its mass, but only on its length.
For the pendulum in this problem, we have
L = 16.8 m
and
(acceleration of gravity)
Therefore the period of this pendulum is
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1) Magnitude of the force:
The magnetic field generated by a current-carrying wire is
where
is the vacuum permeability
I is the current in the wire
r is the distance at which the field is calculated
Using I=135 A, the current flowing in each wire, we can calculate the magnetic field generated by each wire at distance
,
which is the distance at which the other wire is located:
Then we can calculate the magnitude of the force exerted on each wire by this magnetic field, which is given by:
2) direction of the force:
The two currents run in opposite direction: this means that the force between them is repulsive. This can be determined by using the right hand rule. Let's apply it to one of the two wires, assuming they are in the horizontal plane, and assuming that the current in the wire on the right is directed northwards:
- the magnetic field produced by the wire on the left at the location of the wire on the right is directed upward (the thumb of the right hand is directed as the current, due south, and the other fingers give the direction of the magnetic field, upward)
Now let's apply the right-hand rule to the wire on the right:
- index finger: current --> northward
- middle finger: magnetic field --> upward
- thumb: force --> due east --> so the force is repulsive
A similar procedure can be used on the wire on the left, finding that the force exerted on it is directed westwards, so the force between the two wires is repulsive.
The magnetic field generated by a current-carrying wire is
where
I is the current in the wire
r is the distance at which the field is calculated
Using I=135 A, the current flowing in each wire, we can calculate the magnetic field generated by each wire at distance
which is the distance at which the other wire is located:
Then we can calculate the magnitude of the force exerted on each wire by this magnetic field, which is given by:
2) direction of the force:
The two currents run in opposite direction: this means that the force between them is repulsive. This can be determined by using the right hand rule. Let's apply it to one of the two wires, assuming they are in the horizontal plane, and assuming that the current in the wire on the right is directed northwards:
- the magnetic field produced by the wire on the left at the location of the wire on the right is directed upward (the thumb of the right hand is directed as the current, due south, and the other fingers give the direction of the magnetic field, upward)
Now let's apply the right-hand rule to the wire on the right:
- index finger: current --> northward
- middle finger: magnetic field --> upward
- thumb: force --> due east --> so the force is repulsive
A similar procedure can be used on the wire on the left, finding that the force exerted on it is directed westwards, so the force between the two wires is repulsive.