Question

a Review Part A The air-track carts in (Figure 1) are sliding to the right at 1.0 m/s. The spring between them has a spring constant of 100 N/m and is compressed 4.3 cm. The carts slide past a flame that burns through the string holding them together What is the speed of 100-g cart? Express your answer to two significant figures and include the appropriate units. V1 = Value Units Submit Previous Answers Request Answer Figure (< 1 of 1 > X Incorrect; Try Again; 2 attempts remaining Part B String holding carts together What is the direction of the motion of 100-g cart? 100 g VVVV300 g To the left - 1.0 m/s To the right Submit Request Answer

Answer 1

A] Let the final velocities be v1 and v2 respectively,

by momentum conservation,

(m1+m2)*u = m1v1 + m2v2

(0.100+0.300)*1 = 0.100v1 + 0.300v2

Also by energy conservation , 0.5*(m1+m2)u^2 + 0.5kx^2 = 0.5m1v1^2 + 0.5m2v2^2

0.5*(0.100+0.300)*1^2 + 0.5*100*0.043^2 = 0.5*0.100*v1^2 + 0.5*0.300*v2^2

solving the two equations v1 = -0.18 m/s, v2 = 1.4 m/s

speed of cart1 = 0.18 m/s answer

B] to the left, as sign is negative

C] v2 =  1.4 m/s found above

D] to the right, as sign is positive