Forces on a String with a Transverse Wave

AI Thread Summary
The discussion revolves around calculating the total force exerted by the rest of a rope on a section carrying a transverse wave described by the equation y = 0.06 cos(2.1 t - 3.8 x). The problem specifies analyzing a half-wavelength segment of the rope at zero displacement, while neglecting the weight of the rope. Participants note that the horizontal components of force cancel each other out, leaving only the vertical components to consider. The key challenge is determining how to calculate the vertical acceleration from the wave equation. Understanding the relationship between displacement and acceleration is crucial for solving the problem.
Thefox14
Messages
40
Reaction score
0

Homework Statement



The transverse displacement of a harmonic wave on a stretched rope is y = 0.06 cos(2.1 t - 3.8 x), where x and y are in meters and t is in seconds. A 5 meter length of this rope has a mass of 1.5 kg.

[PLAIN]https://wug-s.physics.uiuc.edu/cgi/courses/shell/common/showme.pl?cc/DuPage/phys2111/fall/homework/Ch-16-17-Waves/ec-tran-wave-forces/rope.GIF

At time t = 0, consider a 1/2 wavelength long section of the rope which is carrying the wave between two points which have zero displacement (y = 0). What is the total force exerted by the rest of the rope on this section? (You may neglect any effects due to the weight of the rope.)

Homework Equations



v = \sqrt{\frac{Ften}{\mu}}
\sum F_{net} = ma

The Attempt at a Solution



I'm not sure how to approach this problem. So far what I have realized is that the X component of the force from the left half gets canceled out by the right half. So I really just need to find the Y component right? Though I'm not sure how to go about doing that.

Thanks!
 
Last edited by a moderator:
Physics news on Phys.org
Thefox14 said:
The transverse displacement of a harmonic wave on a stretched rope is y = 0.06 cos(2.1 t - 3.8 x)

It seems like this equation would be a good place to start. If it's giving you the vertical displacement at any point 'x' at a given time then what would be the acceleration of that point?
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
View full post »

Similar threads

Wave function - displacement - transverse wave
Replies
3
Views
2K
Waves and vibrations on a string
Replies
2
Views
2K
Find transverse velocity given an equation of displacement
Replies
9
Views
2K
Waves on a String -- Minimizing reflections from the far end (ring on a bar)
Replies
1
Views
2K
Conservation of power in a traveling wave on a string
Replies
9
Views
2K
Finding Tension in a Transverse Wave on a String
Replies
1
Views
2K
Propagation of transverse pulse on a string
Replies
6
Views
2K
Standing wave transverse motion and amplitude
Replies
5
Views
2K
Time it Takes for a Transverse Pulse to Travel a Distance "L" Up a Cable Against Gravity?
Replies
13
Views
1K
How Do You Calculate Max and Min Transverse Speeds in a Wave on a String?
Replies
1
Views
4K

Hot Threads

Recent Insights

Back
Top