What is the value of ΔVBA=VB−VA if the charge on the plates is 1.00 x 10-9 C, the area of the plates is 2.00 m2 and the distanc
e between points A and B is 5.00 cm? ϵ0=8.85×10−12 C2N⋅m2
1 answer:
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1. 0.42 Hz
The frequency of a simple harmonic motion for a spring is given by:
where
k = 7 N/m is the spring constant
m = 1 kg is the mass attached to the spring
Substituting these numbers into the formula, we find
2. 2.38 s
The period of the harmonic motion is equal to the reciprocal of the frequency:
where f = 0.42 Hz is the frequency. Substituting into the formula, we find
3. 0.4 m
The amplitude in a simple harmonic motion corresponds to the maximum displacement of the mass-spring system. In this case, the mass is initially displaced by 0.4 m: this means that during its oscillation later, the displacement cannot be larger than this value (otherwise energy conservation would be violated). Therefore, this represents the maximum displacement of the mass-spring system, so it corresponds to the amplitude.
4. 0.19 m
We can solve this part of the problem by using the law of conservation of energy. In fact:
- When the mass is released from equilibrium position, the compression/stretching of the spring is zero: , so the elastic potential energy is zero, and all the mechanical energy of the system is just equal to the kinetic energy of the mass:
where m = 1 kg and v = 0.5 m/s is the initial velocity of the mass
- When the spring reaches the maximum compression/stretching (x=A=amplitude), the velocity of the system is zero, so the kinetic energy is zero, and all the mechanical energy is just elastic potential energy:
Since the total energy must be conserved, we have:
5. Amplitude of the motion: 0.44 m
We can use again the law of conservation of energy.
- is the initial mechanical energy of the system, with
being the initial displacement of the mass and
being the initial velocity
is the mechanical energy of the system when x=A (maximum displacement)
Equalizing the two expressions, we can solve to find A, the amplitude:
6. Maximum velocity: 1.17 m/s
We can use again the law of conservation of energy.
- is the initial mechanical energy of the system, with
being the initial displacement of the mass and
being the initial velocity
is the mechanical energy of the system when x=0, which is when the system has maximum velocity,
Equalizing the two expressions, we can solve to find , the maximum velocity:
Answer:
a). 100.2 MHz (typical frequency for FM radio broadcasting)
The wavelength of a frequency of 100.2 Mhz is 2.99m.
b. 1070 kHz (typical frequency for AM radio broadcasting) (assume four significant figures)
The wavelength of a frequency of 1070 khz is 280.3 m.
c. 835.6 MHz (common frequency used for cell phone communication)
The wavelength of a frequency of 835.6 Mhz is 0.35m.
Explanation:
The wavelength can be determined by the following equation:
(1)
Where c is the speed of light, is the wavelength and
is the frequency.
Notice that since it is electromagnetic radiation, equation 1 can be used. Remember that light propagates in the form of an electromagnetic wave.
<em>a). 100.2 MHz (typical frequency for FM radio broadcasting)</em>
Then, can be isolated from equation 1:
(2)
since the value of c is . It is necessary to express the frequency in units of hertz.
⇒
But
Finally, equation 2 can be used:
Hence, the wavelength of a frequency of 100.2 Mhz is 2.99m.
<em>b. 1070 kHz (typical frequency for AM radio broadcasting) (assume four significant figures)</em>
<em> </em>
⇒
But
Finally, equation 2 can be used:
Hence, the wavelength of a frequency of 1070 khz is 280.3 m.
<em>c. 835.6 MHz (common frequency used for cell phone communication) </em>
⇒
But
Finally, equation 2 can be used:
Hence, the wavelength of a frequency of 835.6 Mhz is 0.35m.