Answer:
4/10 of L.
Explanation:
A stopped pipe is a pipe with one closed end and one opened end. it is also called a closed pipe.
The fundamental mode of a stopped pipe is also called its fundamental frequency, and is f₁=v/4L.
Where f₁=fundamental frequency, v= velocity of sound, L= Length of pipe.
The fifth harmonic of the stopped pipe f₅ =5v/4L .................(1)
For an open pipe,
Fundamental mode is also called fundamental frequency f₁₀=v/2l₀ .......... (2)
Where f₁₀ = fundamental frequency of a closed pipe, v= velocity of sound and l₀=length of the resulting open pipe.
from the question, the fundamental mode of the resulting open pipe = The fifth harmonic of the original stopped pipe.
∴ f₅=f₁₀
⇒5v/4L = v/2l₀
Equating v from both side of the equation,
⇒ 5/4L = 1/2l₀
Cross multiplying the equation,
5×2l₀ = 4L× 1
10l₀ = 4L
Dividing both side of the equation by the coefficient of l₀ i.e 10
10l₀/10 = 4L/10
∴ l₀ = 4/10(L)
∴ 4/10 of L must be cut off
Answer:
k = 26.25 N/m
Explanation:
given,
mass of the block= 0.450
distance of the block = + 0.240
acceleration = a_x = -14.0 m/s²
velocity = v_x = + 4 m/s
spring force constant (k) = ?
we know,
x = A cos (ωt - ∅).....(1)
v = - ω A cos (ωt - ∅)....(2)
a = ω²A cos (ωt - ∅).........(3)

now from equation (3)



k = 26.25 N/m
hence, spring force constant is equal to k = 26.25 N/m
Answer:
The level of the root beer is dropping at a rate of 0.08603 cm/s.
Explanation:
The volume of the cone is :

Where, V is the volume of the cone
r is the radius of the cone
h is the height of the cone
The ratio of the radius and the height remains constant in overall the cone.
Thus, given that, r = d / 2 = 10 / 2 cm = 5 cm
h = 13 cm
r / h = 5 / 13
r = {5 / 13} h


Also differentiating the expression of volume w.r.t. time as:

Given:
= -4 cm³/sec (negative sign to show leaving)
h = 10 cm
So,



<u>The level of the root beer is dropping at a rate of 0.08603 cm/s.</u>
Potential Energy = mass * Hight * acceleration of gravity
PE=hmg
PE = 1.5 * .2 * 9.81
PE = 2.943
it lost .6 so 2.943 - .6 = 2.343
now your new energy is 2.343 so solve for height
2.343 = mhg
2.334 = .2 * h * 9.81
h = 1.194
the ball after the bounce only went up 1.194m
To finish one orbit it will take 98 x 60 seconds. So; <span>(2 x pi)/(98 x 60) = 1.07 x 10^-3 rad/sec. </span><span>
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