What is the frequency of a wave having a period equal to 18 seconds? a. 6.6 × 10-2 hertz b. 5.5 × 10-2 hertz c. 3.3 × 10-2 hertz
2 answers:
Answer: Option (b) is the correct answer.
Explanation:
The time taken by a wave crest to travel a distance equal to the length of wave is known as wave period.
The relation between wave period and frequency is as follows.
where, T = time period
f = frequency
It is given that wave period is 18 seconds. Therefore, calculate the wave period as follows.
or,
=
= 0.055 per second (1 cycle per second = 1 Hertz)
or, f =
Thus, we can conclude that the frequency of the wave is .
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Answer:
a) K = 0.63 J, b) h = 0.153 m
Explanation:
a) In this exercise we have a physical pendulum since the rod is a material object, the angular velocity is
w² =
where d is the distance from the pivot point to the center of mass and I is the moment of inertia.
The rod is a homogeneous body so its center of mass is at the geometric center of the rod.
d = L / 2
the moment of inertia of the rod is the moment of a rod supported at one end
I = ⅓ m L²
we substitute
w =
w =
w =
w = 4.427 rad / s
an oscillatory system is described by the expression
θ = θ₀ cos (wt + Φ)
the angular velocity is
w = dθ /dt
w = - θ₀ w sin (wt + Ф)
In this exercise, the kinetic energy is requested in the lowest position, in this position the energy is maximum. For this expression to be maximum, the sine function must be equal to ±1
In the exercise it is indicated that at the lowest point the angular velocity is
w = 4.0 rad / s
the kinetic energy is
K = ½ I w²
K = ½ (⅓ m L²) w²
K = 1/6 m L² w²
K = 1/6 0.42 0.75² 4.0²
K = 0.63 J
b) for this part let's use conservation of energy
starting point. Lowest point
Em₀ = K = ½ I w²
final point. Highest point
Em_f = U = m g h
energy is conserved
Em₀ = Em_f
½ I w² = m g h
½ (⅓ m L²) w² = m g h
h = 1/6 L² w² / g
h = 1/6 0.75² 4.0² / 9.8
h = 0.153 m
Answer:
160 kg
12 m/s
Explanation:
= Mass of first car = 120 kg
= Mass of second car
= Initial Velocity of first car = 14 m/s
= Initial Velocity of second car = 0 m/s
= Final Velocity of first car = -2 m/s
= Final Velocity of second car
For perfectly elastic collision
Applying in the next equation
Mass of second car = 160 kg
Velocity of second car = 12 m/s
Answer:
<em>The new period of oscillation is D) 3.0 T</em>
Explanation:
<u>Simple Pendulum</u>
A simple pendulum is a mechanical arrangement that describes periodic motion. The simple pendulum is made of a small bob of mass 'm' suspended by a thin inextensible string.
The period of a simple pendulum is given by
Where L is its length and g is the local acceleration of gravity.
If the length of the pendulum was increased to 9 times (L'=9L), the new period of oscillation will be:
Taking out the square root of 9 (3):
Substituting the original T:
The new period of oscillation is D) 3.0 T