One end of a spring with a force constant of k 10.0 NVm is attached to the end o

Question

One end of a spring with a force constant of k 10.0 NVm is attached to the end of a long horizontal frictionless track and the other end is attached to a mass m 2.20 kg which glides along the track. After you establish the equilibrium position of the mass spring system, you move the mass in the negative direction (to the left), compressing the spring ecutes simple harmonic motion about the equilibrium position. 1,43 m. You then release the mass from rest and start your stopwatch, that is x(t o) -A, and the mass Determine the following (a) displacement of the mass (magnitude and direction) 1.0 s after it is released (b) velocity of the mass (magnitude and direction) 1.0 s after it is released (c) acceleration of the mass (magnitude and direction) 1.0 s after it is released direction -Select. (d) force the spring exerts on the mass (magnitude and direction) 1.0 s after it is released magnitude (e) How many times does the object oscillate in 12.0s? (Do not round your answer to an integer

Explanation / Answer

(A) m w^2 = k

2.20 w^2 = 10

w = 2.13 rad/s

x = - A cos(wt)

x = - 1.43 cos(2.13t)

Puting t = 1 s

x = - 1.43 cos(2.13 rad) = 0.76 m

mganitude = 0.76 m

direction = +ve x or to the right

(B) v = dx/dt = 1.43 x 2.13 sin(2.13t) = 3.05 m/s sin(2.13t)

at t = 1

v = 2.60 m/s

to the right

(c) a = dv/dt = 6.49 m/s^2 cos(2.13t)

at t = 1 sce

a = - 3.44 m/s^2

magnitude = 3.44 m/s^2

direction - to the left

(D) F = ma = 2.20 x 3.44 = 7.57 N

to the left

(E) T = 2pi / w = 2pi / 2.13 = 2.95 sec

n = t / T = 12 / 2.95 = 4.07 oscillations

Related Questions

Navigate

• Browse (All)
• Browse O
• Subjects

---

---

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