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October 24, 2014

Homework Help: Physics..=> drwls - I need your help

Posted by ~christina~ on Tuesday, February 26, 2008 at 10:26pm.

I need help seeing if my thoughts are correct and how to do some things.

Block 1 of mass 0.200 kg is sliding to the right over a frictionless elevated surface at a speed of 8.00 m / s. The block undergoes an elastic collision with stationary block 2, which is attached to a spring of spring constant 1208.5 N / m. (Assume that the spring does not affect the collision.) After the collision, block 2 oscillates in SHM with a period of 0.140 s, and block 1 slides off the opposite end of the elevated surface landing a distance d from the base of that surface after falling height h = 4.90 m.

(a) Write an expression that gives the displacement of block 2 as a function of time. This expression must include the values of the amplitude of vibration and the angular frequency.

I came up with
x(t)= Acos(omega*t + pi/2)

not sure about +/- for the angle though and how you know which sign to have.(need help on this determination)

I found omega and m2 through: T= 2pi/omega= 2pi sqrt(m/k)

m1v1i + m2v2i = m1v1f + m2v2f
and found v2f and v1f

I was thinking that the v1f I found was the same velocity that the block 1 leaves with and travels off the table with IS THIS CORRECT?

Then I was thinking of using the v1f and v2f in energy equation to find the distance that the spring compresses (Amplitude) so I can plug it into the equation for cos
1/2mv1f + 1/2m2vf = 1/2kx^2
Is this alright?

b) Use differential calculus to obtain expressions for the velocity and acceleration of block 2 as functions of time.
once again I'm not sure if phi's angle or even if phi is correct.

x(t)= A cos (omega*t + pi/2)
v(t)= -omega A sin( omega*t + pi/2)
a(t)= -omega^2 cos (omega*t + pi/2)

c) What are the displacement, velocity, and acceleration of block 2 at t = 0.520 s?
I think I'd just plug into the equation after I find the values from a

(d) What is the value of d?
I know this is projectile motion problem with I think v in x direction...but if it is then would an angle be included? I think yes but I haven't worked with many problems with a object falling after sliding off a level surface.
how would I approach this?

Thank you drwls =)

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