A small 0.180 kg metal ball is tied to a very light (essentially massless) strin

Question

A small 0.180 kg metal ball is tied to a very light (essentially massless) string 0.700 m long to form a pendulum that is then set swinging by releasing the ball from rest when the string makes a 50.0 degree angle with the vertical. Air drag and other forms of friction are negligible.

Part A: What is the speed of the ball when the string passes through its vertical position? v=?

Part B: What is the tension in the string at that instant? T=?

Explanation / Answer

From conservation of energy potential energy at highest point of the pendulum=kinetic energy of the lowest point =>mgh=0.5mv^2 =>v=(2gh)^0.5 where h=l-lcosA where l=0.7, A=50 So h=0.7-0.7cos50=0.25 m Now v=(2*9.8*0.25)^0.5=2.213 m/s Tension T=mg+m(v^2)/l [weight+centrifugal force] =0.18*9.8+0.18(2.213^2)/0.7 =3.02 N

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