Answer to Question #101977 in Mechanics | Relativity for vera

Question

An iron ball of mass 3\,\,kg3kg is hanging at rest tied to the roof by a vertical massless string of length 10m. Then a horizontal force F=14\,\,NF=14N acts on the ball till the ball reaches a point where the string makes an angle of 37 with the vertical. Find the speed of the ball at this instant. (Assume g=10m/s2 sin37=0.6 )

Answer 1

In this case,$h=l-l\ cos\theta=l-l\ cos 37\degree=\frac{l}{5}$

As the gravity is acting opposite to direction of ball,

Net work due to gravity$=-(mgh)=-mg\frac{l}{5}$

Net work done due to applied force$=F\times s=F\times l\ sin\theta$

As per work energy theorem,

Change in Kinetic energy=Net work done

$\frac{1}{2}mv^2=Fl\ sin\theta-mg\frac{l}{5}$

Substituting the values,$\theta=37\degree,F=14N,l=10 m,m=3\ Kg$ ,

$v=4m/sec$