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Simple Harmonic Motion problem?
A 5g bullet is fired horizontally into a 0.50kg block of wood resting on a frictionless table. The block, which is attached to a horizontal spring, retains the bullet and moves forward, compressing the spring. The block-bullet system goes into SHM with a frequency of 9Hz and amplitude of 15cm.
A) Determine the speed of the bullet
1 Answer
- Ossi GLv 71 decade agoFavorite Answer
Hello
Let v1 = velocity of the bullet:
velocity v of the block+bullet= m1*v1/(m1+m2)
v = 0,005v1/0,505
the kinetic energy of the block =
Ek = 1/2 mv^2
Ek = 1/2*0,505*(0,005v1/0,505)^2
find the spring constant k:
ω = 2pif = 2pi*9 = 56,55 rad/s and also
ω = √(k/m)
ω^2 = k/m
k = ω^2*m
k = 56,55^2*0,505
k = 1614,9 N/m
The kinetic energy of the block is = spring energy
1/2*0,505*(0,005v1/0,505)^2 = 1/2*k*s^2
1/2*0,505*(0,005v1/0,505)^2 = 1/2*1614,9*0,15^2
0,000049504v1^2 = 36,3325
v1^2 = 733986,1425
v1 = 856,73 m/s = velocity of the bullet
Regards