A vertical spring with a spring constant of 420 N/m is mounted on the floor. From directly above the spring, which is unstrained
1 answer:
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If l and m both are doubled then the period becomes √2*T
what is a simple pendulum?
It is the one which can be considered to be a point mass suspended from a string or rod of negligible mass.
A pendulum is a weight suspended from a pivot so that it can swing freely.
Here,
A certain frictionless simple pendulum having a length l and mass m
mass of pendulum = m
length of the pendulum = l
The period of simple pendulum is:
Where k is the constant.
Now the length and mass are doubled,
m' = 2m
l' = 2l
Hence,
If l and m both are doubled then the period becomes √2*T
Learn more about Simple Harmonic Motion here:
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Answer:
a) the required time is 0.6283 μs
b) the inductor current is 0.5 mA
Explanation:
Given the data in the question;
The capacitor voltage has its maximum value of 25 V at t = 0
i.e V = V₀ = 25 V
we determine the angular velocity;
ω = 1 / √( LC )
ω = 1 / √( ( 20 × 10⁻³ H ) × ( 8.0 × 10⁻¹² F) )
ω = 1 / √( 1.6 × 10⁻¹³ )
ω = 1 / 0.0000004
ω = 2.5 × 10⁶ s⁻¹
a) How much time does it take until the capacitor is fully discharged for the first time?
V = V₀sin( ωt )
we substitute
25V = 25V × sin( 2.5 × 10⁶ s⁻¹ × t )
25V = 25V × sin( 2.5 × 10⁶ s⁻¹ × t )
divide both sides by 25 V
sin( 2.5 × 10⁶ × t ) = 1
( 2.5 × 10⁶ × t ) = π/2
t = 1.570796 / (2.5 × 10⁶)
t = 0.6283 × 10⁻⁶ s
t = 0.6283 μs
Therefore, the required time is 0.6283 μs
b) What is the inductor current at that time?
(t) = V₀√(C/L) sin(ωt)
{ sin(ωt) = 1 )
(t) = V₀√(C/L)
we substitute
(t) = 25V × √( ( 8.0 × 10⁻¹² F ) / ( 20 × 10⁻³ H ) )
(t) = 25 × 0.00002
(t) = 0.0005 A
(t) = 0.5 mA
Therefore, the inductor current is 0.5 mA
Answer:
The maximum speed at which the car can safety travel around the track is 18.6m/s.
Explanation:
Since the car is in circular motion, there has to be a centripetal force . In this case, the only force that applies for that is the static frictional force
between the tires and the track. Then, we can write that:
And since and
, we have:
Now, if we write the vertical equation of motion of the car (in which there are only the weight and the normal force), we obtain:
Substituting this expression for and solving for
, we get:
Finally, plugging in the given values for the coefficient of friction and the radius of the track, we have:
It means that in its maximum value, the speed of the car is equal to 18.6m/s.