The flying cow problem. Find the period of rotation of the cow.

The rotating cow is attached to the pivot by a string, thus its motion requires a definite period. The period of rotation of the cow is 1.85 s.

The period of rotation of an object is the time that would be required for the object to complete one cycle or revolution.

Thus from the given diagram, let the length of the string holding the cow to the pivot be represented by x. So that applying the Pythagoras theorem, we have:

= +

= +

   = 7225

x =

  = 85

Thus , the length of the string is 85 cm.

So that, the period of rotation of the cow can be determined as follows:

Period, T = 2

where l is the length of the string and g is the gravitational force.

l = x = 85 cm (0.85 m), g = 9.8 m/

Therefore,

T = 2 x x

  = x 0.29451

  = 1.85121

T = 1.85 s

See more about Period of rotation at: link

1.26 s

Explanation:

Draw a free body diagram.  There are three forces: weight force mg pulling down, vertical tension component Tᵧ pulling up, and horizontal tension component Tₓ pulling radially.

Sum of forces in the vertical direction:

∑F = ma

Tᵧ − mg = 0

Tᵧ = mg

Sum of forces in the centripetal direction:

∑F = ma

Tₓ = m v² / r

Tension force must be in the same direction as the string, so:

Tₓ / Tᵧ = 75 / 40

40 Tₓ = 75 Tᵧ

40 m v² / r = 75 mg

8 v² / r = 15 g

v = √(15gr / 8)

Plugging in values:

v = √(15 × 10 m/s² × 0.75 m / 8)

v = 3.75 m/s

The circumference of the path is:

C = 2πr

C = 2π (0.75 m)

C = 4.71 m

So the period is:

t = C / v

t = 4.71 m / 3.75 m/s

t = 1.26 s

Round as needed.

the box does not move because you need to use a force greater than 300 n. you are only using 50 n. it needs to at least be 301 n for the box to move because then it is an unbalanced force and it will move the way that the greater force is pushing it. if you use only 300 n it will be a balanced force and will not move because the force you are exerting on the   box is the same as its force.

hope this !

im sorry if i went too in depth, i am going to include a link to a video on khan academy that will explain this.   hope that you like the video and that it explains more in detail to you.

that is the link.