Answer to Question #347149 in Mechanics | Relativity for Jane

Question

10. A 2.50-kg rock is attached at the end of a thin, very light rope 1.45 m long. You start it

swinging by releasing it when the rope makes an 11° angle with the vertical. You record the observation that it rises only to an angle of 4.5° with the vertical after swings. (a) How much energy has this system lost during that time? (b) What happened to the "lost" energy? Explain how it could have been "lost."

Answer 1

$E_1=mgl(1-\cos\alpha),$

$E_2=mgl(1-\cos\beta),$

$∆E=E_1-E_2=mgl(\cos\beta-\cos\alpha)=0.54~J.$