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A mass of 8kg is suspended from a spring with a spring constant of 16N/m and then released, creating periodic motion. At what di
1 answer:
The spring will come to rest 4.9 m below the natural length
Explanation:
The mass-spring system will come to rest when the restoring force on the spring (pulling upward) balances the weight of the mass (pulling downward). Mathematically, this can be written as
where
k is the spring constant
x is the elongation of the spring
m is the mass
g is the acceleration of gravity
In this problem, we have:
is the mass
is the acceleration of gravity
is the spring constant
Solving the equation for x,
Therefore, the spring will come to rest 4.9 m below the natural length.
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Answer:
(a) The impedance in the circuit is .
(b)The resistance is .
(c) The inuctance is 0.57 H.
Explanation:
(a)
The expression for the impedance is as follows:
Here, is the rms voltage and
is the rms current.
Put and
.
Therefore, the impedance in the circuit is .
(b)
The expression for the average power is as follows;
Here, is the average power and R is the resistance.
Calculate the resistance by rearranging the above expression.
Put and
Therefore, the resistance is .
(c)
The expression for the impedance is as follows;
Here, is the inductive reactance.
Put and
.
The expression for the inductive reactance in terms of frequency is as follows;
Here, L is the inductance.
Calculate the inductance by rearranging the above expression.
Put and f=50Hz.
L=0.57 H
Therefore, the inuctance is 0.57 H.