A 0.700-kg ball is on the end of a rope that is 2.30 m in length. The ball and rope are attached to a pole and the entire apparatus, including the pole, rotates about the pole’s symmetry axis. The rope makes a constant angle of 70.0° with respect to the vertical. What is the tangential speed of the ball?

When the object is moving in circular path a force acting on the body and is directed towards the center around which the body is moving is called as centripetal force.

The ball is acted upon by centripetal acceleration and purpose of acceleration is to vary the direction of motion of the object,

The centripetal force is given by F=mv²/r

From the figure

sinΘ =r/L

r = L sinΘ

r = 2.3 *sin 70°

r = 2.16 m.

As the ball is performing circular motion the centripetal force is given by the horizontal component tension.

According to newton law of motion F=ma

Fₐ = T cos θ = mg

T = mg/ cos θ eqn 1

Fₓ = T sinθ = ma

T sinθ = mv²/r

Sub Value of T from eqn 1

mg sinθ/cosθ=mv²/r

gtanθ = v²/r

Rearranging for v

v =√gr tanθ

v =√9.8*2.16*tan 70°

v = 7.62m/s

The Tangential speed of ball is 7.62 m/s.

tallinn tallinn · Answer 2 · 2022-04-08T16:36:03+02:00

" When The Tangential speed of the ball is = 7.62 m/s To understand more information then check below".

Calculation of Tangential Speed

Given per question

Then, the mass of the ball is = 0.7 kg

The length of the rope is = 2.30 m

Then, the angle made by rope is = 70°

When the object is moving in a circular path a force acting on the body and also is directed towards the center around which the body is moving is called centripetal force.

When The ball is acted upon by centripetal acceleration and also the purpose of acceleration is to vary the direction of motion of the object,

The centripetal force is given by F=mv²/r

From the figure

Then, sinΘ =r/L

After that, r = L sinΘ

Now, r = 2.3 *sin 70°

r is = 2.16 m.

When the ball is performing circular motion the centripetal force is given by the horizontal component tension.

According to newton's law of motion is: F=ma

Then, Fₐ is = T cos θ = m

After that, T is = mg/ cos θ eq. 1

Then, Fₓ is = T sinθ = ma

T sinθ is = mv²/r

Then, Sub Value of T from eq.1

mg sinθ/cosθ=mv²/r

gtanθ = v²/r

Now, Rearranging for v

Then, v =√gr tanθ

After that, v =√9.8*2.16*tan 70°

Then, v = 7.62m/s

Therefore, The Tangential speed of the ball is 7.62 m/s.

Find more information about Tangential Speed here:

https://brainly.com/question/19610415