Answer to Question #171383 in Quantum Mechanics for jaafar aftan

Question

Q3: A spring is mounted linear ,by attaching a spring balanced to

the free end and pulling sideways, we determine that the force of

(4 N ) causes a displacement of 0.02 m .we attach a 2 kg body to

the end ,pull it a side distance of 0.04 m and release it .Find :

1) the force constant of the spring ?

2) the period and frequency of vibration ?

3) compute the maximum velocity attained by the vibrating

body ?

Answer 1

1) F = force applied to pull the spring = 4 N

$x = stretch \space of\space the\space spring = 0.02 m$

$k = spring \space constant$

Using the equation

$F = k x$

$4 = k (0.02)$

$k = \frac{4}{0.02}=200N/m$

2) m = mass of glider = 2.0 kg

Angular frequency is given as $w = \sqrt{\frac{k}{m}}= \sqrt{\frac{200}{2}}= \sqrt{100}=10rad/s$

Frequency is given as $f=\frac{w}{2\pi}=\frac{10}{2\pi}=1.5915 Hz$

Period, $T=\frac{1}{f}=\frac{1}{1.5915}=0.6283$

3) At the extreme position, the mass will have only PE = $0.5 kx^2 = 0.5 ( 200)( 0.04)^2 = 0.16 J$

At the mid position, ( x = 0.02 m), the body will have both KE and PE

$0.16 J = 0.5 ( 200)(0.02)^2 + 0.5 ( 2)( v)^2$

$0.16 = 0.04 + v^2$

$V = 0.346 m/s$