Problem 4 Consider a block attached to a spring, inside a box, as shown in the f

Question

Problem 4 Consider a block attached to a spring, inside a box, as shown in the figure. The block can slide without friction along the bottom of the box. The mass of the block is 0.1 kg, and the spring constant is 40 N/m (a)Suppose you pull the block a distance 5 cm to the right and releasc it. With what angular frequency will it oscillatc? (b)What will be the amplitude of the oscillations? (c)Taking to the right to be positive, at what point in the oscillation is the velocity maximum, and what is its maximum value? (d)At what point in the oscillation is the acceleration maximum, and what is its maximum value? (e)What is the total energy of the spring-block system? (f)lf you take t0 to be the instant when you release the block, write an equation of motion for the oscillation, 2(t) , identifying the values of all constants that you use (g)lmagine now that the box, with the spring and block in it, starts moving to the right with an acceleration a -2m/s2. By how much does the equilibrium position of the block shift (relative to the box), and in what dircction?

Explanation / Answer

4. (a) w = sqrt(k/m) = sqrt(40/0.1) = 20 rad/s

(b) A = 5 cm Or 0.05 m

(c) v will be max. at x = 0

v_max = A w = 0.05 x 20 = 1 m/s

(d) a_max at x = -5 cm and 5 cm

a_max = A w^2 = 20 m/s^2

(e) total energy = k A^2 /2 = 0.05 J

(f) x(t) = 5 cm cos(20 t)

(g) now, Fnet = m a - kx = 0

x = (0.1)(2) /40 =0.005 m Or 0.5 cm

to the left .

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

---

---

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