A spring of negligible mass stretches 3.00 cm from its relaxed length when a force of 8.50 N is applied. A 0.530-kg particle rests on a frictionless h

Yasmin

Yasmin

Answered question

2020-11-14

A spring of negligible mass stretches 3.00 cm from its relaxed length when a force of 8.50 N is applied. A 0.530-kg particle rests on a frictionless horizontal surface and is attached to the free end of the spring. The particle is displaced from the origin to x = 5.00 cm and released from rest at t = 0. (Assume that the direction of the initial displacement is positive.) 
(1) What is the force constant of the spring? 280 N/m 
(2) What are the angular frequency (?), the frequency, and the period of the motion? 
? = 23.121 rad/s 
f = 3.6817 Hz 
T = 0.27161 s 
(3) What is the total energy of the system? 0.35 J 
(4) What is the amplitude of the motion? 5 cm 
(5) What are the maximum velocity and the maximum acceleration of the particle? 
vmax=1.1561ms 
amax=26.73ms2 
(6) Determine the displacement x of the particle from the equilibrium position at t = 0.500 s. 
(7) Determine the velocity and acceleration of the particle when t = 0.500 s. (Indicate the direction with the sign of your answer.) 
v = _________________ ms 
a = _________________ ms2

Answer & Explanation

nitruraviX

nitruraviX

Skilled2020-11-15Added 101 answers

1)k=Fx=283.3N/m
2)w=km==23.121rad/s
f=w2π=3.68Hz
T=1f=0.2717s
3)E=0.5kA2=0.354J
4)5cm
5) vmax=Aw=1.1561ms
amax=Aw2=26.73ms2
6) x=Acos(wt)=5cos(23.1210.5)=2.677cm
7) v=Awsin(wt)=0.9765ms
a=Aw2cos(wt)=14.31ms2
1) F=kx.
8.50=k(3102)
k=283.33Nm1
2) W2=km
W2=2830.530
W=23.16067977rads
3) W=2πT
T={W}{2π} 
T=23.160679772π
T=3.678812717s.
Frequency =1period
=13.678812717
=.272Hz
4) A=5.00cm.
5) V=AWsinWt
max velocity is when t=1.779406359 s
A=5102m
W=23.16067977
V=(5102)(22.16067977)sin(23.160679)
V=1.02ms1
a=AW{ 2}cosWt
max acceleration is when t =0
a=AW2cosWt
 

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