Question

 1 kg block of wood is attached to a spring, of force constant 200 N/m, which is attached to an immovable support. The block rests on a frictional surface with a coefficient of kinetic friction of 0.2. A 20 g bullet is fired into the block horizontally compressing the spring a maximum distance of 15 cm. Find the original velocity of the bullet before the collision.

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Answer 1

Answer:

x=Asin(ωt)

Let x=

2

1

, A=

2

, ω=

T

2π

, T=0.2 sec

Time required to reach wall s given by

2

1

=

2

sin(

0.2

2πt

)

sin(10πt)=

2

1

⇒t=

60

1

solving this we get

t=T/6

Now total time of motion is

t=2×T/6

t=T/3

By problem t=0.2 sec

T=0.6 sec

T=2π∗sqrt(m/k)

By solving we get K=100N/m