Question

A 2kg steel ball hangs on a 8.0-m-long string. The ball is pulled sideways to an angle of 45°, then released. At the very bottom of the swing the ball strikes a 3kg steel block (perfectly elastic collision) that is resting on a frictionless table with a spring (k=20,000 N/m) further down. (a 10 points) To what maximum angle does the ball rebound (degrees)? (b 5 points) What is the compression in the spring (m)?

h XXXX

Answer 1

I suppose height reachso ball 5h, 16 L=8m 2 m2 hie = 0.0936m 29 suppose angle = so h'= 2(1-casco) 1-caso = h = 0.0117 L caso = 1 -0.0117 = 0.988 0 = cos( 6-988) 0=8.776 2 Leaso Domy nou Ih Initial height of ball h= L-Leas &=L(1-caso) n=2.343 m so velocity of ball just before striking the block = √2gh 1 a,= 6.78 m/s suppose velocity of sall after collision = U, =ų velocity of block 1 collision is perfectly elastic so le=1) v-(-6) so tu,= 4, or = 4,-4, using momentum casavation P = Pf m.4i= m₂ų-m, u = m2(4,-4) - mu, so mic, = m₂ up - (mitm₂) U. = (ma-mi) u =(3-2) (6-78) mitm2 5 GF 1.355m/s) = 80135m/s b) kinetic energy of block will be equal to potential energy of compressed spring suppose compression = x Ik x 2 = 1 m 2 ui こ 3 X80135 120000 x=0.0996m