Answer:
0.194 m/s
Step-by-step explanation:
To solve this question, we're going to be using the law of conservation of energy, which is
Kinetic energy of spring before collision = spring energy of spring after compression
Mathematically, we write it as
½mv² = ½kx², where
k is the spring constant of the spring, 85 N/m
m is the mass of the box sliding towards the spring, 9.5 kg
v is the speed of box just before colliding with the spring and is unknown
x is the compression the spring, 6.5 cm = 0.065 m
You should also know that the kinetic energy of the box just before it collides with the spring converts into the spring energy of the spring when it is fully compressed.
½mv² = ½kx²
Substituting the values we'd stated out, we have
½ * 9.5 * v² = ½ * 85 * 0.065²
4.75 * v² = 42.5 * 0.004225
4.75v² = 0.1796
v² = 0.1796 / 4.75
v² = 0.03781
v = √0.03781
v = 0.194 m/s