answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
elena-14-01-66 [18.8K]
2 years ago
14

A tuning fork labeled 392 Hz has the tip of each of its two prongs vibrating with an amplitude of 0.600 mm. A) What is the maxim

um speed of the tip of a prong? B) A housefly (Musca domestica) with mass 0.0270 g is holding on to the tip of one of the prongs. As the prong vibrates, what is the fly's maximum kinetic energy? Assume that the fly's mass has a negligible effect on the frequency of oscillation.
Physics
1 answer:
Leno4ka [110]2 years ago
5 0

To go through one complete wiggle, the tip of the fork has to move outward 0.6mm, then 0.6mm back to the middle, then inward 0.6mm, then 0.6mm back to the middle again.  So one complete wiggle of the tip moves it 2.4mm .

It does this 392 times every second.  So its AVERAGE speed would be

Speed = (distance) x (frequency)

Speed = (2.4 mm) x (392 Hz)

Speed = (0.0024 m) x (392 / sec)  =  0.9408 m/s .

That's the AVERAGE speed of the tip of one prong.  That's easy.  Sadly, the question is asking us for the MAXIMUM speed.  That will be less easy.

Now right here, I'm afraid I will go off the rails for a bit ... I'm going to assert things and do things that I'm not willing to try and explain for 5 points.  It may not even be correct, (which would make it a lot harder to explain).  So I'm just gonna jump in and DO IT.

The way I see it, the tip of that prong is wiggling in sinusoidal wiggles.  Relative to its resting position, its location is something like  

x = (0.6 mm) x sin(2π x 392 t) .

and as usual, its speed is the derivative of that mess.

Speed = dx/dt = (0.6 mm) x (2π x 392) cos(2π x 392 t)

The greatest that the cosine alone can be is 1 , so the maximum value of the speed is

(0.6 mm) x ( (2π x 392))

and that's  1,477.8 mm/s  or  <em>1.4778 m/s</em> .  I think this is the answer to part-a, and now we can go on to consider the hapless fly, stuck by his pads to the wildly oscillating prong.

<u>Part-b </u>is easy.  The fly's maximum kinetic energy is just

KE = (1/2) (flymass) (max speed)²

KE = (1/2) (0.027 g) (1.4778 m/s)²

KE = (1.35 x 10⁻⁵ kg) (2.184 m²/s²)

<em>KE = 2.95 x 10⁻⁵ Joule</em>

So there ya go.  These are my answers and I'm stickin withum.

You might be interested in
A cyclist is riding his bike up a mountain trail. When he starts up the trail, he is going 8 m/s. As the trail gets steeper, he
taurus [48]
-3 m/s
---------
per min

oh I think 8m/s to 3m/s to 0m/s

idk probably -0.08 

7 0
2 years ago
Read 2 more answers
Two flywheels of negligible mass and different radii are bonded together and rotate about a common axis (see below). The smaller
jeka94

Answer:

Explanation:

Torque on smaller wheel

= F x r

50 x .30

= 15 Nm

Torque on larger wheel

= F x .5

For equilibrium

F x .5 = 15

F = 15 / .5

= 30 N

8 0
2 years ago
How much force is required to drag a 90 lb. box up this "frictionless" inclined plane? 109 lb. 10 lb. 81 lb. 9 lb.
MrRissso [65]
I believe is 10 lb if not it's 9 lb.
5 0
2 years ago
Read 2 more answers
Air at 3 104 kg/s and 27 C enters a rectangular duct that is 1m long and 4mm 16 mm on a side. A uniform heat flux of 600 W/m2 is
ad-work [718]

Answer:

T_{out}=27.0000077 ºC

Explanation:

First, let's write the energy balance over the duct:

H_{out}=H_{in}+Q

It says that the energy that goes out from the duct (which is in enthalpy of the mass flow) must be equals to the energy that enters in the same way plus the heat that is added to the air. Decompose the enthalpies to the mass flow and specific enthalpies:

m*h_{out}=m*h_{in}+Q\\m*(h_{out}-h_{in})=Q

The enthalpy change can be calculated as Cp multiplied by the difference of temperature because it is supposed that the pressure drop is not significant.

m*Cp(T_{out}-T_{in})=Q

So, let's isolate T_{out}:

T_{out}-T_{in}=\frac{Q}{m*Cp}\\T_{out}=T_{in}+\frac{Q}{m*Cp}

The Cp of the air at 27ºC is 1007\frac{J}{kgK} (Taken from Keenan, Chao, Keyes, “Gas Tables”, Wiley, 1985.); and the only two unknown are T_{out} and Q.

Q can be found knowing that the heat flux is 600W/m2, which is a rate of heat to transfer area; so if we know the transfer area, we could know the heat added.

The heat transfer area is the inner surface area of the duct, which can be found as the perimeter of the cross section multiplied by the length of the duct:

Perimeter:

P=2*H+2*A=2*0.004m+2*0.016m=0.04m

Surface area:

A=P*L=0.04m*1m=0.04m^2

Then, the heat Q is:

600\frac{W}{m^2} *0.04m^2=24W

Finally, find the exit temperature:

T_{out}=T_{in}+\frac{Q}{m*Cp}\\T_{out}=27+\frac{24W}{3104\frac{kg}{s} *1007\frac{J}{kgK} }\\T_{out}=27.0000077

T_{out}=27.0000077 ºC

The temperature change so little because:

  • The mass flow is so big compared to the heat flux.
  • The transfer area is so little, a bigger length would be required.
3 0
2 years ago
A particle moving in the x direction is being acted upon by a net force F(x)=Cx2, for some constant C. The particle moves from x
elixir [45]

Answer:

Change in kinetic energy is ( 26CL³)/3

Explanation:

Given :

Net force applied, F(x) = Cx²  ....(1)

Displacement of the particle from xi = L to xf = 3L.

The work-energy theorem states that change in kinetic energy of the particle is equal to the net amount of work is done to displace the particle.

That is,

ΔK = W = ∫F·dx

Substitute equation (1) in the above equation.

ΔK =  ∫Cx²dx

The limit of integration from xi = L to xf = 3L, so

\Delta K=\frac{C}{3}(x_{f} ^{3} - x_{i} ^{3})

Substitute the values of xi and xf in the above equation.

\Delta K=\frac{C}{3}((3L) ^{3} - L ^{3})

\Delta K=\frac{C}{3}\times26L^{3}

5 0
2 years ago
Other questions:
  • How would reversing the wheel’s initial direction of rotation affect the result??
    6·1 answer
  • A boat's capacity plate gives the maximum weight and/or number of people the boat can carry safely in certain weather conditions
    11·1 answer
  • Why doesn't a ball roll on forever after being kicked at a soccer game?
    6·2 answers
  • Another term for electromotive force is _____.<br><br> voltage<br> current<br> resistance<br> power
    7·1 answer
  • Moving water, like that of a river, carries sediment as it moves along its bed. The faster the water flows, the more sediment th
    13·2 answers
  • A person kicks a ball, giving it an initial velocity of 20.0 m/s up a wooden ramp. When the ball reaches the top, it becomes air
    12·1 answer
  • An object executes simple harmonic motion with an amplitude A. (Use any variable or symbol stated above as necessary.) (a) At wh
    9·1 answer
  • If revenue is $3,000 and operating expenses are $4,000, cash flow equals _____. -$1,000 $1,000 -$7,000 $7,000
    8·1 answer
  • dopasuj wartości pracy z ramki do przedstawionych sytuacji ,a nastepnie wyraż te prace w dżulach uwaga jedna wartośc pracy nie b
    15·1 answer
  • Which illustration represents the arrangement of particles in a gas?
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!