An ant sits on a cd at a distance of 17 cm from the center. If it sits there for 42
1 answer:
Answer:
a) N = 8.54[rev]; b) v = 21.73 [m/s]; c) T = 4.918[s]; d) 12.2[rev/min]
Explanation:
We know that the arc length is calculated by the following expression:
L = α * r
where:
r = radius = 17 [cm] or 0.17 [m]
α = 360° or 2*pi [rad] = 6.283 [rad]
L = (6.283*0.17) = 1.068 [m] = 106.81 [cm] is the distance travelled in one revolution of the CD
a) N = number of revolutions
N = 913 / 106.81
N = 8.54 [rev]
b ) The speed can be calculated by the following expression:
v = d/t
Where:
d = distance = 913[cm]
t = time = 42[sec]
v = 913/42 = 21.73 [cm/s]
c)
We have the number of revolutions and the time therefore we can calculate the number of revolutions per second
w = 8.54 / 42 =0.2033 [rev/s]
And we know that the period is the reciprocal of the time
T = 1 / 0.2033
T = 4.918 [s]
d )
We need to convert from [rev/s] into [rev/min]
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Answer:
0.143 m
Explanation:
The relationship between force applied on a string and stretching of the spring is given by Hooke's law:
where
F is the force exerted on the spring
k is the spring constant of the spring
x is the stretching of the spring from its equilibrium position
In this problem, we have:
F = 20 N is the force applied on the spring
k = 140 N/m is the spring constant
Solving for x, we find how far the spring will stretch:
The thermal efficiency is defined as follows
,
and the energy which is put into the system is
.
In your case
So
which gives an efficiency of
.
and the energy which is put into the system is
In your case
So
To solve this problem it is necessary to apply the concepts related to wavelength as a function of frequency and speed, as well as to determine the wavelength as a function of length.
From the harmonic vibration generated we know that the total length of the string will be equivalent to a half of the wavelength, that is
Where,
Wavelength
Therefore the wavelength for us would be,
From the relationship of speed, frequency and wavelength we know that
Therefore the speed of the wave is 232.75m/s