Answer:
22.4 cm
Explanation:
The total mechanical energy of the particle Etot = K + U where K = kinetic energy = 1/2mv² where m = mass of particle = 100 g =0.1 kg and v = speed of particle = 2 m/s and U = potential energy = 1/2kx² where k = spring constant and x = displacement
Etot = K + U
U = Etot - K
U = Etot - 1/2mv²
Since Etot = 0.45 J, substituting the values of the other variables into the equation, we have
U = Etot - 1/2mv²
U = 0.45 J - 1/2 × 0.1 kg × (2 m/s)²
U = 0.45 J - 1/2 × 0.1 kg × 4 m²/s²
U = 0.45 J - 0.1 kg × 2 m²/s²
U = 0.45 J - 0.2 J
U = 0.25 J
Now U = 1/2kx² and the angular frequency ω = √(k/m) ⇒ ω²m = k
So, U = 1/2ω²mx²
x² = 2U/ω²m
x = (√2U/m)/ω
since ω = 10 rad/s, substituting the values of the variables into the equation, we have
x = (√2U/m)/ω
x = (√2 × 0.25 J/0.1 kg)/10 rad/s
x = (√0.5 J/0.1 kg)/10 rad/s
x = (√5 J/kg)/10 rad/s
x = 2.24/10 m
x = 0.224 m
x = 22.4 cm
