Question

1. A spring of negligible mass and force constant k = 400N/m is hung vertically, and a 0.200-kg pan is suspended from its lower end. A butcher drops a 2.2-kg steak onto the pan from a height of 0.40 m. The steak makes a totally inelastic collision with the pan and sets the system into vertical SHM.

A) What is the speed of the pan and steak immediately after the collision?

B) Suppose the mass of the steak is halved, the subsequent amplitude of motion would change by what factor?

a. Factor of 1/?2 times

b. Factor of 1/2 times

c. Factor of 2 times

d. Factor of ?2 times

e. None of the above

C) Suppose the spring constant of the spring is increased by 2 times, the subsequent amplitude of motion would change by what factor?

a. Factor of 1/?2 times

b. Factor of 1/2 times

c. Factor of 2 times

d. Factor of ?2 times

e. None of the above

Answer 1

initial speed of steak is

vi = sqrt 2 gh= sqrt 2 ( 9.8) 0.4 = 2.8 m/s

Apply conservation of momntum,the speed of the pan and steak immediately after the collision is

m1 u+ m2 vi = ( m1 + m2)v

v= m1 u+ m2 vi / m1 + m2

= 0.2(0) + 2.2(2.8)/ 0.2+2.2

= 2.56 m/s

(b)

Apply conservation of energy

1/2 k x^2 = (1/2 ( m1 + m2) v^2

x= sqrt ( m1 + m2) v^2/k

= sqrt ( 0.2+2.2)( 2.56)^2/400

=0.198 m

su poose mass of the seak is halved

x'= sqrt ( 0.2+1.1)( 2.56)^2/400

=0.145m

x'/x = 0.145/0.198 = 0.7323

non of the above is correct option(e) is correct answer

when k' = 2k = 800

x'=sqrt ( 0.2+2.2)( 2.56)^2/800

=0.140 m

x'/x = 0.140/0.198 = 0.707

x' = sqrt 2* x

option (d) is correct answer