Question

Two carts of equal mass, m = 0.280 kg, are placed on a
frictionless track that has a light spring of force constant k =
51.9 N/m attached to one end of it.
The red cart is given an initial velocity of v0 = 3.50 m/s to
the right, and the blue cart is initially at rest. If the carts
collide elastically,
a)find the magnitude of the velocity of the red cart just after the first collision.

b)Find the magnitude of the velocity of the blue cart just after the first collision.

c)Find the maximum compression in the spring.

Answer 1

In an eleastic collion of two bodies of equal mass, they two bodies exchange velocities. That way, both momentum and kinetic energy are conserved. The blue cart has a final velocity of zero.

The red cart acquires a speed of Vo = 3.50 m/s and heads for the spring, I assume.

Maximum spring compression X is achieved when
(1/2) kX^2 = (1/2) M Vo^2
X = Vo sqrt(M/k)

Answer 2

Thanks.
But as the carts exchange their velocities,blue cart must have a velocity = 3.50 m/s & red car zero velocity.
Am i right?
And
x = 3.5sqrt(0.280/51.9 = 0.26 m

Answer 3

correct.

Answer 4

how do u do part A and B?