Answer:
f1 = 12.90 Hz
Explanation:
To calculate the first harmonic frequency you use the following formula for n = 1:
( 1 )
It is necessary that the unist are in meters, then you have:
L: length of the string = 60cm = 0.6m
M: mass of the string = 0.05kg
T: tension on the string = 20 N
you replace the values of L, M and T in the expression (1) for getting f1:
Hence, the first harmonic has a frequency of 12.90 Hz
Answer:
The required angular speed the neutron star is 10992.32 rad/s
Explanation:
Given the data in the question;
mass of the sun M
= 1.99 × 10³⁰ kg
Mass of the neutron star
M
= 2( M )
M = 2( 1.99 × 10³⁰ kg )
M = ( 3.98 × 10³⁰ kg )
Radius of neutron star R = 13.0 km = 13 × 10³ m
Now, let mass of a small object on the neutron star be m
angular speed be ω.
During rotational motion, the gravitational force on the object supplies the necessary centripetal force.
GmM = / R² = mRω²
ω² = GM = / R³
ω = √(GM = / R³)
we know that gravitational G = 6.67 × 10⁻¹¹ Nm²/kg²
we substitute
ω = √( ( 6.67 × 10⁻¹¹ )( 3.98 × 10³⁰ ) ) / (13 × 10³ )³)
ω = √( 2.65466 × 10²⁰ / 2.197 × 10¹²
ω = √ 120831133.3636777
ω = 10992.32 rad/s
Therefore, The required angular speed the neutron star is 10992.32 rad/s
Answer:
ωi = 15.4 rev/sec
Explanation:
Since the movement of the fan is rotating, we are thus dealing with Rotational motion. In rotational motion, for angular speed to take place also means angular acceleration is also occurring.
angular acceleration = α = (change in speed)/(change in time)
angular acceleration = α = Δw/Δt = (ω - ωi) /(t- t₀) ..........(equation 1)
α = (ω -ωi) /(t- 0)
α = (ω-ωi) /t
ωi = ω - αt ......................................(equation 2)
where ωi is the initial angular speed.
We replace the values for ω, t and α
ωi = 105 rad/sec - ( 4.4 rad/sec² )(1.85s) = 96.86 rad/s = 15.415747788 rev/sec
The total displacement is equal to the total distance. For the east or E direction, the distance is determined using the equation:
d = vt = (22 m/s)(12 s) = 264 m
For the west or W direction, we use the equations:
a = (v - v₀)/t
d = v₀t + 0.5at²
Because the object slows down, the acceleration is negative. So,
-1.2 m/s² = (0 m/s - 22 m/s)/t
t = 18.33 seconds
d = (22 m/s)(18.33 s) + 0.5(-1.2 m/s²)(18.33 s)²
d = 201.67 m
Thus,
Total Displacement = 264 m + 201.67 m = 465.67 or approximately 4.7×10² m.
