Ahorizontal spring with stiffness 0.4 n/m has a relaxed length of 11 cm (0.11 m). a mass of 21 grams (0.021 kg) is attached and you stretch the spring to a total length of 27 cm (0.27 m). the mass is then released from rest. what is the speed of the mass at the moment when the spring returns to its relaxed length of 11 cm (0.11 m)?

0.6983 m/s

Explanation:

k = spring constant of the spring = 0.4 N/m

L₀ = Initial length = 11 cm = 0.11 m

L = Final length = 27 cm = 0.27 m

x = stretch in the spring = L - L₀ = 0.27 - 0.11 = 0.16 m

m = mass of the mass attached = 0.021 kg

v = speed of the mass

Using conservation of energy

Kinetic energy of mass = Spring potential energy

(0.5) m v² = (0.5) k x²

m v² = k x²

(0.021) v² = (0.4) (0.16)²

v = 0.6983 m/s

the force required to move the cart is divided by three or 33.33 n.