A string of mass m=.1kg is stretched to where its length is L=20m. What is the tension force applied to the string if it takes a pulse 2 seconds to get from one end to the other?
m=kg
L=20m
T=4s
mass density =m/L = .1/20 = kg/m
Tension =?
I know v=sqrt(F_t/mass density) But I'm given two unknowns. How would I find velocity?
Well, you said v = sqrt(F/.005)
you also said the pulse goes 20 m in 2 s
so
v = 20/2 = 10 m/s
so
10 = sqrt (F/.005)
100 = F/.005
F = .5 N
To solve for the tension force in the string, we first need to find the velocity of the pulse traveling through the string.
In this case, the velocity of the pulse can be obtained using the formula:
velocity (v) = distance (L) / time (t)
Given that the distance is equal to the length of the string (L = 20m) and the time taken by the pulse to travel that distance is 2 seconds, we can substitute these values into the formula to find the velocity.
v = L / t
v = 20m / 2s
v = 10 m/s
Now that we have the velocity, we can move on to finding the tension force in the string.
The formula for calculating the tension force (T) is:
Tension = mass density (μ) * velocity squared (v^2)
Given that the mass of the string (m) is 0.1 kg and the length (L) is 20m, we can calculate the mass density (μ) as:
mass density (μ) = m / L
μ = 0.1 kg / 20 m
μ = 0.005 kg/m
Now, we can substitute the values of velocity (v) and mass density (μ) into the formula to find the tension force (T).
T = μ * v^2
T = 0.005 kg/m * (10 m/s)^2
T = 0.005 kg/m * 100 m^2/s^2
T = 0.5 N
Therefore, the tension force applied to the string is 0.5 Newtons.