A block of mass 0.1 kg is attached to a spring of spring constant 21 N/m on a fr

Question

A block of mass 0.1 kg is attached to a spring of spring constant 21 N/m on a frictionless track. The block moves in simple harmonic motion with amplitude 0.13 m. While passing through the equilibrium point from left to right, the block is struck by a bullet, which stops inside the block.The velocity of the bullet immediately before it strikes the block is 61 m/s and the mass of the bullet is 2.41 g.
A) Find the speed of the block immediately before the collision.
Answer in units of m/s
B) If the simple harmonic motion after the collision is described by x = B sin(? t + f), what is the new amplitude B?
Answer in units of m
C) The collision occurred at the equilibrium position.How long will it take for the block to reach maximum amplitude after the collision?
Answer in units of s

Explanation / Answer

given : block amplitude (A) = 0.13 m
k = 21 N/m
so block have potential energy = 0.5*k*A2 = 0.17745 joule.

(a) as the surface is frictionless so energy will conserve, so at mean position the block have kinetic energy will be same as the potential energy at its extremies. potential energy are totally converted to kinetic energy.

so at mean position before collision,

0.5*m*v2 = 0.17745 j

v = 1.8838 m/s

(b) so on collision we can apply linear momentum conservation law

0.1*1.8838 + 0.00241*61 = (0.1+0.00241)*v

v = 3.2749 m/s (velocity of block + embeded bullet)

so at this position the kinetic energy of the system will be

K.E. = 0.5*(0.1+0.00241)*(3.27492) = 0.549 joule.

again due to energy conservation law at the new extremies the potential energy of the embeded system will be this K.E. which is equal to,

0.5*21*B2 = 0.549

B = 0.2286 m

(c) = (k/m) (where m is the embeded mass)

T (period of oscillation) = 2*/

so the time to reach the maximum amplitude will be T/4 = /(2*) = (*m)/(2*k) = 0.1096 s.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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