Answer:
0.832 m/s
Explanation:
The work done by the spring W equals the kinetic energy of the object K
The work done by the spring W = 1/2k(x₀² - x₁²) where k = spring constant, x₀ = initial compression = 0.065 m and x₁ = final compression = 0.032 m
The kinetic energy of the object, K = 1/2mv² where m = mass of object and v = speed of object
Since W = K,
1/2k(x₀² - x₁²) = 1/2mv²
k(x₀² - x₁²) = mv²
mv² = k(x₀² - x₁²)
v² = [(k/m)(x₀² - x₁²)]
taking square root of both sides, we have
v = √[(k/m)(x₀² - x₁²)] since ω = angular frequency = √(k/m),
v = √[(k/m)√(x₀² - x₁²)]
v = ω√(x₀² - x₁²)]
Since ω = 14.7 rad/s, we substitute the other variables into the equation, so we have
v = 14.7 rad/s × √((0.065 m)² - (0.032 m)²)]
v = 14.7 rad/s × √(0.004225 m² - 0.001024 m²)]
v = 14.7 rad/s × √(0.003201 m²)
v = 14.7 rad/s × 0.056577
v = 0.832 m/s
