Question

A simple pendulum bob at rest is struck by a bat so that it is just able to loop round once. Find the velocity

Answer 1

point is equal to total energy, Equate both

1/2 mv₁² = 1/2 mv₂² + mgl -----→(i)

1/2 m√(10)² = 1/2 mv₂² + mgl

v₂² = 8 gl .

Now the tension at the horizontal position.

(b) Assume that the velocity at y = v₃

Similarly like equation (i) , at y and velocity v₃

1/2mv₁² = 1/2mv₃² + mg(2 l )

v₃² = 6mgl

Now thew tension

-mg

 × mg

(c)Assume the velocity at z = v₄ .

Again similarly like equation (i) at z = v₄

1/2mv₁² = 1/2mv₄² +mgh    ∵[h = l(1+cosθ)]

Now,

1/2 mv₁² =1/2 mv₄² +mgl(1+cos60°)

calculating it , we get

v₄² =7gl

Now the tension ,

-mg(cos60°) .

On calculating , we get

 = 7mg -0.5mg 

= 6.5 mg