A ski gondola is connected to the top of a hill by a steel cable of length 720 m and diameter 1.3 cm. As the gondola comes to the end of its run, it bumps into the terminal and sends a wave pulse along the cable. It is observed that it took 14 s for the pulse to return.

What is the speed of the pulse?

What is the tension in the cable?

The wave speed is 2*720/14 = 103 m/s

103 m/s = sqrt(T/a)
where a is the mass of cable per length. You will need the density of steel and the cable radius to get a.

a = pi (D^2/4)*(steel density)
Make sure it is in kg/m

Then solve for T , which will be in Newtons

To find the speed of the pulse, we can use the formula:

speed = distance / time

The distance traveled by the pulse is equal to the length of the cable, which is given as 720 m. The time taken for the pulse to travel back and forth along the cable is 14 s.

Therefore, the speed of the pulse is:

speed = 720 m / 14 s = 51.43 m/s

To find the tension in the cable, we can use the relationship between tension, wave speed, and the linear mass density of the cable. The linear mass density (μ) of the cable is given by the mass of the cable per unit length.

To calculate the linear mass density, we first need to find the mass of the cable. The volume of the cable can be calculated using the formula for the volume of a cylinder:

volume = π * (radius)^2 * length

The diameter of the cable is given as 1.3 cm, so the radius (r) can be calculated by dividing the diameter by 2:

radius = 1.3 cm / 2 = 0.65 cm = 0.0065 m

Now we can calculate the volume of the cable:

volume = π * (0.0065 m)^2 * 720 m = 0.159 m^3

The density of steel is approximately 7850 kg/m^3. Multiplying the volume by the density will give us the mass of the cable:

mass = volume * density = 0.159 m^3 * 7850 kg/m^3 = 1247.35 kg

The linear mass density of the cable is then given by:

linear mass density (μ) = mass / length = 1247.35 kg / 720 m = 1.732 kg/m

Finally, we can find the tension in the cable using the formula:

tension = wave speed^2 * linear mass density

Substituting the values we calculated:

tension = (51.43 m/s)^2 * 1.732 kg/m = 4481.73 N

Therefore, the tension in the cable is approximately 4481.73 Newtons.