Two astronauts are tethered together on a space walk and rotate around each other. they each weigh 82 kg and are 114 m apart. what is the tension (in newton) on the cable if the period of the rotation is 45 s?

Using the formula for centripetal force, which is provided by the tension in the cable, the tension in the tether connecting two 82 kg astronauts rotating with a radius of 57 m and period of 45 seconds is approximately 88.4 Newtons.

Explanation:

To determine the tension on the cable between two rotating astronauts in space, we can use the concept of centripetal force which is provided here by the tension in the cable. The formula to calculate this tension (T) is given by:

T

= (4 π² m r) / T²

where:

m is the mass of each astronaut,
r is the radius of the circle, which is half the distance between them,
T is the period of rotation.

In the student's question, each astronaut's mass (m) is 82 kg, they are 114 m apart (so the radius r = 114/2 = 57 m), and the rotational period (T) is 45 seconds.

Substituting these values in, we find the tension (T):

T

= (4 π² 82 kg 57 m) / (45 s)²

After calculating this, the tension on the cable is approximately 88.4 Newtons.