a) Two blocks of masses m = 2 kg and M = 5 kg are placed on a horizontal, fricti

Question

a) Two blocks of masses m = 2 kg and M = 5 kg are placed on a horizontal, frictionless surface. A massless spring having a force constant of k = 1120 N/m is attached to one of them, and the blocks are pushed together with the spring between them, as shown in the figure below. A string used to hold them together is burned, after which the block of mass M moves to the right with a speed of 3 m/s. If the two blocks were initially at rest just prior to the string being burned, what is the final speed of the block of mass m? (Ans: 7.5 m/s)

b) In a different experiment, m is moving to the right with a speed of 10 m/s and M is also moving to the right but at a speed of 3 m/s. When the blocks collide, what is the maximum compression of the spring? (Ans: 0.25 m)

Length of spring is not given

Explanation / Answer

given

a )

m = 2 kg

M = 5 kg

k = 1120 N/m

vM = 3 m/s

using conservation of linear momentum

- m vm + M vM = 0

vm = ( M X vM / m )

vm = 5 X 3 / 2

vm = 15 / 2

vm = 7.5 m/sec

b )

uisng equation

x = ( m M ( vm - vM )2 / k ( m + M ) )1/2  

x = ( 2 X 5 X ( 10 - 3 )2 / 1120 X ( 2 + 5 ) )1/2

x = ( 490 / 7840 )1/2

x = 1/4

x = 0.25 m

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