Multiple choice, no details required or graded. The figure shows a block of mass

Question

Multiple choice, no details required or graded. The figure shows a block of mass m = 2.0 kg attached to a spring with spring constant k on a frictionless surface. The block is pushed to the left to position x = -0.5m and, at time t = 0, it is released from rest and starts oscillating with a period of 2.0 s. (a) Which of the following equations describes the position (in units of meter) as a function of time? [1] x(t) = -0.5 cos(pt) [2] x(t) = 0.5 sin(pt) [3] x(t) = 0.5 cos(2t) [4] x(t) = -0.5 sin(2pt) [5] none of these (b) What is the maximum speed of the block? [1] nu_max = (p^2/4) m/s [2] nu_max = (p/2) m/s [3] nu_max = 2 m/s [4] nu_max = 2p^2 m/s [5] none of these (c) What is the spring constant of the spring? [1] k = (p^2/4) N/m [2] k = (p/2) N/m [3] k = 2 N/m [4] k = 2p^2 N/m [5] none of these (d) What is the total energy of the system? [1] E = (p^2/4) J [2] E = (p/2) J [3] E = 2 J [4] E = 2p^2 J [5] none of these

Explanation / Answer

as the block is pushed to left, the displacement is -ve at t= 0

a)

x(t) = -0.5*cos(pt)

option (a)

(b)

at x = 0.5 PE is max

pE = 0.5*k*x^2

k = m*p^2

PE = 0.5*m*p^2*x^2

at x =0 KE is max

KE = 0.5*m*v^2

from energy conservation

KE = PE

0.5*m*v^2 = 0.5*m*p^2*x^2

v^2 = p^2*x^2

v^2 = p*x = p*0.5 = p/2 m/s

option [2]

+++++++++

(c)

k = (p^2*x)

k = p^2/2 N/m

option [2]

++++++++++

d)

Total energy E = KEmax or PE max = 0.5*m*p^2*x^2

TE = 0.5*2*p^2*0.5^2 = p^2/4 J

option [1]

Related Questions

Navigate

• Browse (All)
• Browse M
• Subjects

---

---

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