3. A bored shuttle astronaut swings a 3.0 kg Crescent wrench around in a circle of radius R = 1.5 m on the end of a tether with constant speed. Each revolution of the wrench takes 0.75 seconds. A) Find the tension in the tether. B) Find the work done by the tension on the wrench in one complete revolution. Sketch the wrench at an instant and think about θ. What is cos θ? Alternatively, think about the displacement for a complete circle.

A) Tension = 316 N

B) Work done = 0J

Explanation:

We are given;

Mass; m = 3kg

Radius; r = 1.5m

Time to complete one revolution; t = 0.75 seconds.

A) we know that in uniform circular motion,

Force due to tension towards the centre is given by;

F_t = mv²/r

Where,

m = mass

v = velocity

r = radius.

Now, in uniform circular motion,

Velocity is given by; v = 2πr/t

Thus, v = (2π * 1.5) / 0.75

v = 12.566 m/s

Thus, Tension is now;

F_t = (3 * 12.566²) / 1.5 ≈ 316 N

B) work done in thus case, would be gotten from the formula;

W = (F_t) * d*cosθ

Where:

F_t is tension

d is distance

θ is the angle

Since motion is towards the centre of the circle, thus, d = 0.

So, W = 316 * 0 * cos θ

W = 0J