As the spring is compressed, it performs
-1/2 (252 N/m) (0.118 m)² ≈ -1.75 J
of work on the clay, while gravity does
(0.263 kg) (9.80 m/s²) (0.118 m) ≈ 0.304 J
on it. Then the total work W performed on the clay ball is approximately -1.45 J.
By the work-energy theorem, W is equal to the change in the clay ball's kinetic energy ∆K. If v is the speed with which it hits the spring, then
W = ∆K
-1.45 J = 0 - 1/2 mv²
Solve for v :
-1.45 J = -1/2 (0.263 kg) v²
v² ≈ 11.0 m²/s²
v ≈ 3.32 m/s
