Solving a Physics Problem: Transverse Wave Travel Time

[lmar769]

Homework Statement

Algebra based physics: A 23 kg mass is suspended from the bottom of a rope of length 2.4 m and mass 17 kg. The acceleration of gravity is 9.8 m/s^2.
Find time for a transverse wave to travel the length of the rope. Answer in units of sec.

Homework Equations

u= mass rope/ length rope
F=mg
v= d/t

The Attempt at a Solution

u= 17kg / 2.4m = 7.0833333

v= sqr (17+23)(9.8)/7.0833333
v= 7.439165039

t= d/v
t= 2.4m / 7.439165039
t= 0.322616851 s

This answer is wrong and I've had 2 tutors look over this but couldn't figure where the problem is.

 

[Gear300]

The mass of the rope is the medium the tension distributes across but it is not the source of the tension...although, if you want to be a bit more certain...you could use a bit of calculus to find the tension at various parts of the rope (it does change along its length...but you probably don't need to take this into account).

 

[baba89]

I would approach this problem by first identifying the key variables and equations needed to solve it. The key variables in this problem are the mass of the rope, the length of the rope, and the acceleration of gravity. The equation that relates these variables is F=mg, where F is the force due to gravity, m is the mass, and g is the acceleration of gravity.

Using this equation, we can calculate the force due to gravity on the rope:
F = (17 kg + 23 kg) * 9.8 m/s^2 = 392.4 N

Next, we need to consider the properties of a transverse wave, which is the type of wave that will travel along the rope. The speed of a transverse wave is given by the equation v = √(T/μ), where T is the tension in the rope and μ is the linear mass density of the rope. The linear mass density is calculated by dividing the mass of the rope by its length.

In this problem, we are given the mass and length of the rope, so we can calculate the linear mass density as:
μ = 17 kg / 2.4 m = 7.08333 kg/m

Now, we can use this value to calculate the speed of the wave:
v = √(392.4 N / 7.08333 kg/m) = 10.798 m/s

Finally, we can use the equation v = d/t to find the time it takes for the wave to travel the length of the rope. Rearranging the equation, we get:
t = d/v = 2.4 m / 10.798 m/s = 0.222 sec

Therefore, the time it takes for the transverse wave to travel the length of the rope is 0.222 seconds. It's important to check the units in our final answer to make sure they are correct. In this case, we are given the acceleration of gravity in units of m/s^2, so our final answer should also be in seconds.

In conclusion, the key to solving this physics problem is to identify the relevant variables and use the appropriate equations to calculate the time it takes for a transverse wave to travel the length of the rope. By carefully considering the units and using the correct equations, we can arrive at the correct answer.