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?

The Tangential speed of ball is 7.62 m/s

Explanation:

Given are

 mass of the ball 0.7 kg

 length of rope is 2.30 m

 angle made by rope is 70°

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.

does anyone know or what?