If the block moves a distance 1.8 cm to the right after the bullet passed throug

Question

If the block moves a distance 1.8 cm to the right after the bullet passed through it, find the speed v at which the bullet emerges from the block.

Answer in units of m/s 

If the block moves a distance 1.8 cm to the right after the bullet passed through it, find the speed v at which the bullet emerges from the block. Answer in units of m/s A bullet of mass 5 g moving with an initial speed 400 m/s is fired into and passes through a block of mass 2 kg, as shown in the figure. The block, initially at rest on a frictionless, horizontal surface, is connected to a spring of force constant 443 N/m.

Explanation / Answer

Let mass of bullet as m, mass of block as M ; initial speed of bullet as v1 ; initial speed of block as v2

speed of bullet after impact as v1' ; speed of block after impact as v2'

Linear momentum is conserved :

m.v1 + M.v2 = m.v1' + M.v2'

(5x10-3).(400) + 2(0) = 5x10-3.v1' + 2.v2'

2 = 5x10-3.v1' + 2.v2' ............(1)

K = spring potensial energy

0.5.M.v2'2 = 0.5.k.x2

(v2') = (kx2/M) = [443.(1.8x10-2)2/2] = 0.268 m/s

subsitute v2' into eq (1) we get :

2 = 5x10-3.v1' + 2.(0.268)

v1' = 292.8 m/s

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

---

---

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