Answered

IDNLearn.com provides a seamless experience for finding the answers you need. Our community is ready to provide in-depth answers and practical solutions to any questions you may have.

[3 marks]
A particle of mass 100 g executes simple harmonic motion about x = 0 with angular frequency ω = 10 s-1. Its total mechanical energy is Etot = 0.45 J. Find the displacement of
the particle when its speed is 2 m/s. [3 marks]​

Sagot :

Oladayoademosuidn

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

We appreciate every question and answer you provide. Keep engaging and finding the best solutions. This community is the perfect place to learn and grow together. IDNLearn.com has the solutions to your questions. Thanks for stopping by, and come back for more insightful information.