A-ball-of-mass-1-kg-moving-with-velocity-3-m-s-collides-with-spring-of-natural-length-2-m-and-force-constant-144-N-m-What-will-be-length-of-compressed-spring-

Question Number 23518 by Tinkutara last updated on 01/Nov/17

A ball of mass 1 kg moving with velocity

3 m / s collides with spring of natural

length 2 m and force constant 144 N / m .

What will be length of compressed

spring ?

Commented by Tinkutara last updated on 01/Nov/17

{Book}^{'} s answer : 1.5 m

Mine : 1.75 m

Which is right ?

Commented by mrW1 last updated on 01/Nov/17

case 1 :

\frac{1}{2} {mv}^{2} = \frac{1}{2} k Δ^{2}

Δ = v \sqrt{\frac{m}{k}} = 3 \sqrt{\frac{1}{144}} = \frac{3}{12} = \frac{1}{4} = 0.25 m

L_{2} = L - Δ = 2 - 0.25 = 1.75 m

case 2 :

\frac{1}{2} {mv}^{2} + mg Δ = \frac{1}{2} k Δ^{2}

k Δ^{2} - 2 mg Δ - {mv}^{2} = 0

\Rightarrow Δ = \frac{2 mg + \sqrt{{4 m}^{2} g^{2} + {4 kmv}^{2}}}{2 k}

\Rightarrow Δ = \frac{mg + \sqrt{m^{2} g^{2} + {kmv}^{2}}}{k} = \frac{10 + \sqrt{100 + 144 \times 9}}{144} = 0.32 m

L_{2} = L - Δ = 1.68 m

Commented by Tinkutara last updated on 01/Nov/17

Thank you very much Sir!

What is the reason for case 2 ?

Commented by mrW1 last updated on 01/Nov/17

case 2 is the case in that the spring is

compressed mostly . that is when the

mass hits the spring vertically with a

speed v . i just wanted to see if the

spring could be compressed 0 . 5 m even

in the worst case .

Commented by mrW1 last updated on 01/Nov/17

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