A block of mass 0.3 kg is attached to a
spring of spring constant 23 N/m on a fric-
tionless track. The block moves in simple har-
monic motion with amplitude 0.2 m. While
passing through the equilibrium point from
left to right, the block is struck by a bullet,
which stops inside the block.
The velocity of the bullet immediately be-
fore it strikes the block is 68 m/s and the mass
of the bullet is 4.67 g.
Find the speed of the block immediately
before the collision.
Answer in units of m/s.
If the simple harmonic motion after the collision is described by x = B sin(wt + O), what
is the new amplitude B?
Answer in units of m.
.5(m)(v^2) + .5(k)(x^2) = .5(k)(A^2)
w = 2 (pie) (frequency) = [(2)(pie)]/(Period)
frequency = (2)(pie)(square root[k/mass])
The Attempt at a Solution
I have some ideas on how to solve the problem, but just need some guidance on if I'm doing it right and if my thinking process is right.
Since they're wanting me to find the speed of the block before the the bullet impacts it, then would I just neglect the information about the bullets?
And in the equation, how would you find x? Would you just halve the amplitude to find the x?
Part 2: The O is supposed to be a O with a vertical line in the middle of it. Not sure what that letter is called, but it looks like the greek letter, Phi. Tell me if I'm thinking this out right. I can use the frequency formula for a spring and solve for "f" and plug it back into the omega formula. Once I get the Omega, I'll plug that number into the simple harmonic motion equation. Is this right so far? But when using "m" in the frequency formula, what value of mass should I use? I'm thinking about combining the two masses, block + bullet, because the bullet is embedded into the block, creating a new system. Is this right also?
But after doing all this, how would I go about and solve for the amplitude, B. For what value should I use for "x"?