A collision leaves less energy for the spring

A 1 kg cart at 4 m/s sticks to a stationary 1 kg cart at the natural-length position of a horizontal 100 N/m spring between the second cart and a fixed stop. Collision duration is negligible. The smooth track allows the combined carts to compress the spring.

Find the maximum compression.

Organize the givens & assumptions

m₁ = m₂ = 1 kg
u₁ = 4 m/s
k = 100 N/m

g is irrelevant on the smooth horizontal track; negligible spring impulse during the brief sticking collision; spring's far end fixed; ideal spring afterward.

A $\sqrt2/5\ \mathrm m$
B $0.40\ \mathrm m$
C $0.20\ \mathrm m$
D $0.080\ \mathrm m$

Try it on paper first. Free sample problems in every collection include the complete reasoning: find one in this collection →