The figure depicts two carts set on a flat track. On the left is a smaller cart labeled capital A with a rightward velocity labeled lower-case v subscript zero. On the right there is a larger block labeled capital B.Two carts are set on a flat track and roll without friction. Cart A rolls with initial velocity v­0 toward cart B which is at rest. The center of mass of the two-cart system has a velocity vcm,i before the carts collide and vcm,f after the carts collide. In which of the following situations will vcm,i = vcm,f?

a) k= 827.5N/m

b) L = 0.67m

Explanation:

a)

we know that:

F = kx

where F is the force execute in the spring, k the spring constant and x the change in the length of the spring, so:

mg = kx

where m is the mass of the object and g is the gravity. Replacing values, we get:

(7.6kg*9.8) = K(0.4m-0.31m)

Solving for k:

k = 827.5N/m

b) First, we plus the forces of the two people as:

F = 150N + 150N

F = 300N

Finally, using the following equation:

F = Kx

300N = 827.5N/m(x)

Solving for x:

x = 0.36m

It means that the new length of the spring is:

L = 0.36m+0.31m

L = 0.67m