Impulse steel ball falling on steel slab

[offbeatjumi]

Homework Statement

mass of steel ball = 40g = .04 kg
h1 = 2.00 m
h2 = 1.60 m
A steel ball is dropped from height of 2.00 m onto horizontal steel slab, rebounds to height of 1.60m. Calculate impulse of ball during impact.

Homework Equations

impulse J = F*dt
J = P2 - P1
I tried using

The Attempt at a Solution

I tried using equations of kinematics to solve for the velocities of the ball before and after impact, to then find the final and initial momentum, and solve for impulse by finding change in momentum.
I have the answer from the back of the book, 0.47 N*s. But I did not get that answer with my method. How should I approach this? Thanks.

 

[kuruman]

Your method is correct. It is probably its implementation that is incorrect. Maybe you missed a minus sign, maybe you punched in the wrong numbers. If you show the details of your calculation, someone might be able to locate where you went wrong.

 

[offbeatjumi]

I divided it in two steps, step one before impact and step two after impact.

in step one:

I use v(f)^2 = v(i)^2 - 2gy
v(f)^2 = 0 - (-39.2)
v(f) = -sqrt(39.2) = v(1)
P(1) = mv(1) = -.2504 kg*m/s

in step two:
I use the same kinematic equation
v(f)^2 = v(1)^2-2gy
v(f)^2 = 39.2 - 2*(-9.8)*1.60 = 70.56
v(f) = 8.4 m/s = v(2)
P(2) = mv(2) = 0.336

P(2) - P(1) = 0.336 - (-.2504) = 0.5863 N*m

answer should be 0.47 N*m
??

 

[kuruman]

The complete kinematic equation is

$$v^{2}_{f}=v^{2}_{i}+2a(x_{f}-x_{i})$$

Here v_f is the speed when the object is at position x_f and v_i is the speed when the object is at x_i.

We assume that position is measured from the slab.

For step 1, x_i=2.00 m, x_f=0, v_i=0, a = -9.8 m/s² and we are looking for v_f, the speed of the ball just before it hits the slab on its way down. This gives

$$v^{2}_{f}=0^{2}+2(-9.8\;m/s^2)(0 - 2.00\;m)$$

If you do the calculation, you get -.2504 kg*m/s for the momentum as you have already found.

The problem with your solution is the identification of the variables after the bounce. After the bounce the speed of the ball at x_i = 0 is the unknown speed v_i. What is the speed v_f when the position is x_f = 1.60 m?

 

[offbeatjumi]

thank you very much

yeah i did not assign the correct positions/velocities of the ball to the equation, i see now that the final velocity in the second situation is zero