Blocks A (mass 2.00 k g ) and B (mass 10.50 k g ) move on a frictionless, horizo

Question

Blocks A (mass 2.00kg ) and B (mass 10.50kg ) move on a frictionless, horizontal surface. Initially, block B is at rest and block A is moving toward it at 10.0m/s . The blocks are equipped with ideal spring bumpers. The collision is head-on, so all motion before and after the collision is along a straight line. Let +x be the direction of the initial motion of A.

A) Find the maximum energy stored in the spring bumpers and the velocity of each block at that time.

Find the maximum energy.

B) Find the velocity of A

C) Find the velocity of B

A

Explanation / Answer

A)

Energy stored in spring will be maximum when kinetic energy of blocks is minimum, This happens when both blocks have relative velocity = 0,

So Let velocity of each block be v m/s in + x direction

Conservation of momentum gives:

2*10 = (2+10.5)*v

v = 20/12.5 = 1.6 m/s

Final kinetic energy = (1/2)*(2+10.5)*(1.6^2) = 16 J

Initial Kinetic Energy = (1/2)*2*(10^2) = 100J

So, maximum energy stored in spring = 100- 16 = 84 J

Part B and C)

Let velocities after collision is complete be Va and Vb resepectively in + ve x direction.

Conservation of momentum gives,

2*10 = 2*Va + 10.5*Vb

Va = (20-Vb*10.5)/2 .............(1)

Conserving energy,

100 = (1/2)*2*Va^2 + (1/2)*10.5*Vb^2

100 = Va^2 + 5.25*Vb^2   ...........(2)

Substituting this in (1) in (2)

100 = 20^2 + 110.25Vb^2 - 420Vb +5.25Vb^2

-300 = 115.5Vb^2- 420Vb

Gives,

Vb = 4.247 m/s

from (1)

Va = -0.611 m/s

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