A 5.00-kg object is attached to a spring and placed on a frictionless, horizonta
ID: 1949861 • Letter: A
Question
A 5.00-kg object is attached to a spring and placed on a frictionless,horizontal surface. A horizontal force of 17.0 N is
required to hold the object at rest when it is pulled 0.3 m
from its equilibrium position (the origin of the x axis). The
object is now released from rest from this stretched position,
and it subsequently undergoes simple harmonic oscillations.
Find (a) the force constant of the spring, (b) the
frequency of the oscillations, and (c) the maximum speed
of the object. (d) Where does this maximum speed occur?
(e) Find the maximum acceleration of the object. (f) Where
does the maximum acceleration occur? (g) Find the total
energy of the oscillating system. Find (h) the speed and
(i) the acceleration of the object when its position is equal
to 0.4 the maximum value.
Explanation / Answer
Mass m = 5 kg Force F = 17 N Amplitude A = 0.3 m (a) The force constant of the spring k = F /A = 56.666 N / m (b) The frequency of the oscillations f = /2 Where = angular frequency = [ k / m] = 3.366 rad / s So, f = 0.535 Hz (c) The maximum speed V = A = 1.01 m / s (d) Maximum speed occur at equilibrium position (e) The maximum acceleration of the object = A 2 = 3.4 m / s 2 (f) The maximum acceleration occur at expreme positions (g)The total energy of the oscillating system E = ( 1/ 2) m 2 A 2 = 2.55 J (h) The speed of the object when its position is equal to 0.4 the maximum value is v = [ A 2 - x 2 ] Where x = 0.4 A v = x 0.91651 = 3.085 m / s Required accleration a ' = x 2 = 0.4 A 2 = 1.36 m / s 2 = 1.36 m / s 2Related Questions
Hire Me For All Your Tutoring Needs
Integrity-first tutoring: clear explanations, guidance, and feedback.
Drop an Email at
drjack9650@gmail.com
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.