Question

Two friends hold on to a rope, one at each end, on a smooth, frictionless ice surface. They skate in a circle about an axis through the center of the rope and perpendicular to the ice. The mass of one friend is 81.0 kg and the other has a mass of 125.0 kg. The rope of negligible mass is 4.5 m long and they move at a speed of 4.50 m/s.

(a) What is the magnitude of the angular momentum of the system comprised of the two friends? kg · m2/s

(b) They now pull on the rope and move closer to each other so that the rope between them is now half as long. Determine the speed with which they move now. m/s

(c) The two friends have to do work in order to move closer to each other. How much work did they do? J

Answer 1

.a) We define the system as formed by two friends and rope

L = L1 +L2 = m1 v1 r + m2 v2 r v is perpendicular L = r x p

. m1=85 Kg        m2= 125 Kg v1=v2=v =4.50 m/s       r =L/2= 4.5/2 = 2.25 m

L = (m1+m2) v r                   L = (85+125) 4.5 2.25

L = 2126 Kg m²/s

.b)   

L2= Lo/2          

As the forces are internal total L is preserved

. r2= L2/2      r= 4.5 /2 2 =1.125 m

L = (m1+m2) v r2        v= L / (( m1+m2)r2)        v= 2126 / (210   1.125)=

. v= 9 m/s

.c)

W = F d = delt K = Kf- Ko

Ko = ½ (m1+m2) v_o²     Ko = ½ (85+125) 4.5²     Ko= 1923.75 J

Kf = ½ (85+125) 9²    Kf= 7695 J

W = Kf-Ko = 7695 -1923     

W= 5772 J