Calculate the rate of loss of heat through a glass window of area 200 CM square and thickness 0.5 CM where temperature inside is
1 answer:
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Answer:
<u>Part A</u>
I = 1.4 mW/m²
<u>Part B</u>
β = 91.46 dB
Explanation:
<u>Part A</u>
Sound intensity is the power per unit area of sound waves in a direction perpendicular to that area. Sound intensity is also called acoustic intensity.
For a spherical sound wave, the sound intensity is given by;
Where;
P is the source of power in watts (W)
I is the intensity of the sound in watt per square meter (W/m2)
r is the distance r away
Given:
P = 34 W,
A = 1.0 cm²
r = 44 m
The sound intensity at the position of the microphone is calculated to be;
I = 0.0013975 W/m²
≈ I = 0.0014 W/m² = 1.4 × 10⁻³ W/m²
I = 1.4 mW/m²
The sound intensity at the position of the microphone is 1.4 mW/m².
<u>Part B</u>
Sound intensity level or acoustic intensity level is the level of the intensity of a sound relative to a reference value. It is a a logarithmic quantity. It is denoted by β and expressed in nepers, bels, or decibels.
Sound intensity level is calculated as;
β dB
Where,
β is the Sound intensity level in decibels (dB)
I is the sound intensity;
I₀ is the reference sound intensity;
By pluging-in, I₀ is 1.0 × 10⁻¹² W/m²
∴ β
β
β = 91.46 dB
The sound intensity level at the position of the microphone is 91.46 dB.
Answer:
6.86 m/s
Explanation:
This problem can be solved by doing the total energy balance, i.e:
initial (KE + PE) = final (KE + PE). { KE = Kinetic Energy and PE = Potential Energy}
Since the rod comes to a halt at the topmost position, the KE final is 0. Therefore, all the KE initial is changed to PE, i.e, ΔKE = ΔPE.
Now, at the initial position (the rod hanging vertically down), the bottom-most end is given a velocity of v0. The initial angular velocity(ω) of the rod is given by ω = v/r , where v is the velocity of a particle on the rod and r is the distance of this particle from the axis.
Now, taking v = v0 and r = length of the rod(L), we get ω = v0/ 0.8 rad/s
The rotational KE of the rod is given by KE = 0.5Iω², where I is the moment of inertia of the rod about the axis of rotation and this is given by I = 1/3mL², where L is the length of the rod. Therefore, KE = 1/2ω²1/3mL² = 1/6ω²mL². Also, ω = v0/L, hence KE = 1/6m(v0)²
This KE is equal to the change in PE of the rod. Since the rod is uniform, the center of mass of the rod is at its center and is therefore at a distane of L/2 from the axis of rotation in the downward direction and at the final position, it is at a distance of L/2 in the upward direction. Hence ΔPE = mgL/2 + mgL/2 = mgL. (g = 9.8 m/s²)
Now, 1/6m(v0)² = mgL ⇒ v0 =
Hence, v0 = 6.86 m/s
Answer:
a) See attached picture, b) We know the initial velocity = 0, initial position=0, time=12.0s, acceleration=, c) the car travels 172.8m in those 12 seconds, d) The car's final velocity is 28.8m/s
Explanation:
a) In order to draw a sketch of the situation, I must include the data I know, the data I would like to know and a drawing of the car including the direction of the movement and its acceleration, just like in the attached picture.
b) From the information given by the problem I know:
initial velocity =0
acceleration =
time = 12.0 s
initial position = 0
c)
unknown:
displacement.
in order to choose the appropriate equation, I must take the knowns and the unknown and look for a formula I can use to solve for the unknown. I know the initial velocity, initial position, time, acceleration and I want to find out the displacement. The formula that contains all this data is the following:
Once I got the equation I need to find the displacement, I can plug the known values in, like this:
after cancelling the pertinent units, I get that my answer will be given in meters. So I get:
which solves to:
So the displacement of the car in 12 seconds is 172.8m, which makes sense taking into account that it will be accelerating for 12 seconds and each second its velocity will increase by 2.4m/s.
d) So, like the previous part of the problem, I know the initial position of the car, the time it travels, the initial velocity and its acceleration. Now I also know what its final position is, so we have more than enough information to find this answer out.
I need to find the final velocity, so I need to use an equation that will use some or all of the known data and the unknown. In order to solve this problem, I can use the following equation:
Next, since I need to find the final velocity, I can solve the equation just for that, I can start by multiplying both sides by t so I get:
and finally I can add to both sides so I get:
and now I can proceed and substitute the known values:
which solves to:
