Conservation (energy and momentum) problem

[N_L_]

I'm having trouble with the following experiment. A balloon filled with sand attached to a string swings and hits a tissue box, which then slides to a stop. A spring scale is used to pull the box across the table and the amount of force required is given. The goal is to find the coefficient of friction between the box and the table two ways and then to compare.

http://paer.rutgers.edu/pt3/experiment.php?topicid=4&exptid=141

Part I

The mass of the balloon and tissue box are given. From a short movie you are given the amount of force required by the spring scale.

Box - 161.1 g
Spring scale reading - .25 N

Drawing an FBD gave Fn up, Fg down, Fapp to the right and FF to the left.

Sum Fext=ma
Fg + Fn + Fapp + FF=ma

x) -FF + Fapp = ma
y) Fn-Fg=0

The mass is given as 161.1g = .1611 kg

we read from the spring scale that the Fapp= .25 Newtons

-m*g*mu + .25 = .1611-a
(.1611)(9.8)(mu) + .25 = -.1611a
1.579 mu = .1611a + .25
mu = .1020a + .1583

Is this right so far? Should I just set the equations equal to zero instead...how do you find acceleration then?


Part II

Slide distance after being struck by the balloon - 27.9 cm
Balloon - 54.7 g
Estimated height of the balloon's center of mass - 6.75 cm
Height from which the pendulum balloon is released - 76.1 cm

The directions say to use conservation of energy and momentum to solve.

Momentum:

[mass of box * velocity of box before] + [mass of balloon pendulum * velocity of balloon pendulum before] = [mass of box * velocity of box after] + [mass of balloon pendulum * velocity of balloon pendulum after]

Zero + 54.7vtwo = 161.1voneprime + 54.7vtwoprime

Energy: Before the pendulum is released all of its energy is potential. The box doesn't have kinetic energy or potential energy. If I focus on just the balloon pendulum I can find its velocity just before impact with the box (vtwo) in the above equation. Vtwo = 1.22 m/s

From there, I'm not sure what to do or where exactly to apply conservation of energy (from what starting point to what ending point...). I'm also not sure how to use Q in my energy equation.

Any ideas?

 

[Hootenanny]

For part one, I would think that you could assume constant velcocity. (But don't take my word on that).

For part two, I think you would use conservation of energy to find the velocity of the balloon just before it hit the tissue box (potental to kinetic) rather than trying to measure it.

~H