Question

A small body tied to a string is revoled in a verticle circle of radious 0.8m such
that its speed of the top of circle is 4m/s. Find the maximum speed of the body
during the motion?​

Answer 1

Answer:

6.88 or 6.9 m/s

Explanation: Maximum velocity is at the point where PE = 0, at the bottom.

  Let the mass of the body be m.

At the highest point:  

height = 2r = 2(0.8) = 1.6  ;  u(velo.) = 4 m/s

 Total energy = KE + PE

            = mgh + 1/2 mu²

            = m(9.8*1.6 + 1/2 (4)² )    

            = (23.68)m

At the lowest point: h = 0 , let velocity = v

Total energy = mg(0) + 1/2 mv²

          (23.68)m = 0 + 1/2 m v²

           23.68 = 1/2 v²

           47.36 = v²

           6.88 m/s = v

Since velocity at the bottom is maximum, maximum velocity is 6.88 m/s

Answer 2

Answer:

Given :-

• A small body tied to a string is resolved in a vertical circle of radius 0.8 m such that its speed of the top of circle is 4 m/s.

To Find :-

• What is the maximum speed of the body.

Solution :-

First, we have to find the total energy :

As we know that :

➲ Total Energy = Kinetic Energy + Potential Energy

Given :

• Radius = 0.8 m

Now we have to find the height :

Height = 2r

Then,

↦ Height = 2(0.8)

↦ Height = 1.6

• Initial velocity (u) = 4 m/s
• Acceleration due to gravity (g) = 9.8 m/s²

Now, according to the question by using the formula we get,

↦ Total Energy = mgh + ½ mu²

↦ Total Energy = m × 9.8 × 1.6 + ½ × (4)²

↦ Total Energy = m × 15.68 + ½ × 16

↦ Total Energy = m × 15.68 + 8

↦ Total Energy = m × 23.68

➠ Total Energy = 23.68 m

Now, we have to find the maximum speed of the body :

Given :

• Total Energy = 23.68 m

According to the question :

↦ Total Energy = ½ m(v)² + mg+(0)

↦ 23.68 m = ½ mv² + 0

↦ 23.68 = ½ v²

↦ 23.68 × 2 = v²

↦ 47.36 = v²

↦ √47.36 = v

↦ 6.88 = v

➠ v = 6.88 m/s

∴ The maximum speed of the body is 6.88 m/s.