A 12.5 kg box sliding on a frictionless flat surface tuns into a fixed spring which compresses at a distance x = 14.1 cm. the spring constant is 94.5 kN/m Find the initial speed of the box

12.3 m/s

Explanation:

m = mass of the box sliding on frictionless flat surface = 12.5 kg

x = compression of the spring = 14.1 cm = 0.141 m

k = spring constant = 94.5 kN/m = 94500 N/m

v = initial speed of the box

Using conservation of energy

Kinetic energy of the box = Spring potential energy

(0.5) m v² = (0.5) k x²

m v² = k x²

Inserting the values

(12.5) v² = (94500) (0.141) ²

v = 12.3 m/s