A spring scale hung from the ceiling stretches by 6.4 cm when a 2.0 kg mass is hung from it. The 2.0 kg mass is removed and repl
1 answer:
In the first case, the force acting on the spring is the weight of the mass:
This force causes a stretching of
on the spring, so we can use these data to find the spring constant:
In the second case, the first mass is replaced with a second mass, whose weight is
And since we know the spring constant, we can calculate the new elongation of the spring:
This force causes a stretching of
In the second case, the first mass is replaced with a second mass, whose weight is
And since we know the spring constant, we can calculate the new elongation of the spring:
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Answer:
3. velocity is zero.
Explanation:
The velocity of a simple harmonic motion is given by
Here, <em>ω</em> is the angular velocity, <em>A</em> is the amplitude (or maximum displacement from the equilibrium point) and <em>x</em> is the displacement at any time.
At maximum displacement, <em>x </em>=<em> A</em>.<em> </em>Then
Therefore, at maximum displacement, velocity is 0.
Practically, this can be observed in a simple pendulum. As it approaches the maximum displacement, its velocity reduces. It becomes zero at this point and then reverses as the pendulum changes course. Then the velocity begins to increase. It becomes maximum at the equilibrium point but once past that, the velocity begins to reduce as it approaches the other amplitude.
For acceleration,
It follows that at maximum displacement, the acceleration is a maximum. The negative sign indicates that it is in an opposite direction to the displacement. Both kinetic energy () and linear momentum (
) are proportional to velocity; they are therefore both zero at the maximum displacement.
Given Information:
Resistance = R = 14 Ω
Inductance = L = 2.3 H
voltage = V = 100 V
time = t = 0.13 s
Required Information:
(a) energy is being stored in the magnetic field
(b) thermal energy is appearing in the resistance
(c) energy is being delivered by the battery?
Answer:
(a) energy is being stored in the magnetic field ≈ 219 watts
(b) thermal energy is appearing in the resistance ≈ 267 watts
(c) energy is being delivered by the battery ≈ 481 watts
Explanation:
The energy stored in the inductor is given by
The rate at which the energy is being stored in the inductor is given by
The current through the RL circuit is given by
Where τ is the the time constant and is given by
Therefore, eq. 1 becomes
At t = 0.13 seconds
(b) thermal energy is appearing in the resistance
The thermal energy is given by
(c) energy is being delivered by the battery?
The energy delivered by battery is