A phone cord is 2.85 m long. The cord has a mass of 0.254 kg. A transverse wave pulse is produced by plucking one end of the taut cord. The pulse makes four trips down and back along the cord in 0.758 s.
What is the tension in the cord?
To find the tension in the cord, we can use the formula:
T = (m * v^2) / L
where T is the tension, m is the mass of the cord, v is the velocity of the pulse, and L is the length of the cord.
First, let's find the velocity of the pulse. The pulse travels the length of the cord four times in 0.758 s. Therefore, the time taken for one complete trip down and back is 0.758 s / 4 = 0.1895 s.
The velocity of the pulse can be found using the formula:
v = 2L / t
where v is the velocity, L is the length of the cord, and t is the time taken for one complete trip.
Substituting the given values into the formula, we have:
v = 2 * 2.85 m / 0.1895 s
v = 30 m/s
Now, let's calculate the tension in the cord using the formula:
T = (m * v^2) / L
Substituting the given values into the formula, we have:
T = (0.254 kg * (30 m/s)^2) / 2.85 m
T = (0.254 kg * 900 m^2/s^2) / 2.85 m
T = 8.0916 N
Therefore, the tension in the cord is approximately 8.0916 N.