Question

A 20 kg child is on a swing that hangs from 3.8-m-long chains. What is her maximum speed if she swings out to a 42 ? angle?

Answer 1

Here it is given that child is of 20KG and on the swing which is 3.8m long and we have to find maximum speed when swing makes a 42? angle.

To solve this question we have to use Conservation of energy equation

Which states that

E= K.E + P.E= Constant Where K.E= kinetic energy and P.E=Potential energy

During, swing there are two stages so, first we have to find hieght of swing the from initial stage

So, hieght is L-Lcos(teta) i.e. (3.8-3.8cos42?) Where L= Length of swing

Now When the swing is at the maximum position then K.E energy is zero

P.E= mgh= mg(3.8-3.8cos42?)= constant Where m=Mass of child and g= Gravitational constant(9.8)

Now when swing come back P.E is zero

K.E=constant

1/2mv^2=mg(3.8-3.8cos42?) Where v= velocity

so, v^2= 9.8*0.97

v(maximum)= 3m/s

So, the maximum speed the child swing is 3m/s