A block of mass m = 0.830 kg isfastened to an unstrained horizontal spring whose

Question

A block of mass m = 0.830 kg isfastened to an unstrained horizontal spring whose spring constantis k = 88.5 N/m. The block isgiven a displacement of +0.120 m, where the + sign indicates thatthe displacement is along the +x axis, and then releasedfrom rest. (a) What is the force (magnitude and direction)that the spring exerts on the block just before the block isreleased?
1 N

(b) Find the angular frequency of the resultingoscillatory motion.
2 rad/s

(c) What is the maximum speed of the block?
3 m/s

(d) Determine the magnitude of the maximum acceleration of theblock.
4 m/s2
(a) What is the force (magnitude and direction)that the spring exerts on the block just before the block isreleased?
1 N

(b) Find the angular frequency of the resultingoscillatory motion.
2 rad/s

(c) What is the maximum speed of the block?
3 m/s

(d) Determine the magnitude of the maximum acceleration of theblock.
4 m/s2

Explanation / Answer

a. According to Hooke's law
          F =-k*x
             = -(88.5 N/m) *(0.120 m)              = 10.62 N
The negative sign indicates that force is a response to thedisplacement so it will be in the opposite direction of thedisplacement.

b. angulary frequency = (k/m)                                     = 88.5/0.830                                     = 10.32 rad /s

c. According to conservation of energy we have
               0.5kx2 = 0.5mv2
                       v = x                           = 10.32* 0.120                            =1.238m/s d. a = 2x = 12.78m/s2

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.