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A bullet of mass m moving with a velocity v collides head on with a block of mass m which is placed on a car of mass 4m. Bullet gets embedded in the block. The block is connected with car by massless spring of constant k. Find the maximum compression x of the spring. Neglect friction everywhere.

A bullet of mass m moving with a velocity v collides head on with a block of mass m which is placed on a car of mass 4m. Bullet gets embedded in the block. The block is connected with car by massless spring of constant k. Find the maximum compression x of the spring. Neglect friction everywhere.

Grade:12

2 Answers

AJIT AskiitiansExpert-IITD
68 Points
11 years ago

Dear Abdul , Always apply the two principles given below , trying with the force approach maybe complex,

Momentum conservation:

momemtum of bullet = momentum of (bullet + mass m +car)

mv =(m+m+4m) .v2

therefore , v2 = v/6

energy conservation:

 k.e of energy of bullet  = k.e of ( car +mass+ bullet ) + p.e of spring

1/2 * m* v= 1/2*(m+m+4m)*(v/6)2  + 1/2 *k *x2

5mv2/6 =  kx2

x = (5mv2/6k)1/2

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Abdul Qadeer
18 Points
11 years ago

Sir,

Thanks alot for spending your precious time. My approach is exactly same as yours. But unforunately the answer is not correct.

the correct answer is x=v(m/3k)^1/2

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