Hello, Please be as detailed as possible in showing step-by-step answers so I ca

Question

Hello,

Please be as detailed as possible in showing step-by-step answers so I can understand.

Q: A 5.0 kg block is attached to a spring (k = 400 N/m) that is attached to a wall. The block sits motionless on a frictionless surface. A bullet of mass m = 100.0g is travelling at a speed of 100.0 m/s and strikes the wood of the block and embeds itself into the block. This block/bullet system the oscillates.

1) What is the velocity of the block immediately after the bullet strikes it (and is embeded into the block)?

2) WHat is the amplitude of oscillations?

3) What is the frequency of oscillations?

4) What is the maximum acceleration of the block/bullet system when it is oscillating?

Please show formulas, and maybe a quick explanation.

People who are strong in physics are encouraged to reply!

Thanks

Explanation / Answer

1)

let m1 = 0.1 kg , u1=100 m/s
m2 = 5 kg.
according to law of conservation of momentum

m1*u1 = (m1+m2)*v

v = m1*u1/(m1+m2)

v = 0.1*100/(0.1+5) = 1.96 m/s

2)let A is the amplitude

0.5*k*A^2 = 0.5*(m1+m2)*v^2

0.5*k*A^2 = 9.8 J

A = 0.22 m

3) w = sqrt(k/m) = 8.85 rad/s


f = w/2*pi = 1.41 HZ

4)

a_max = F/(m1+m2) = k*A/(m1+m2) = 17.36 m/s^2

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