# Physics C Mech. 3 2008 Help!

1. Jan 28, 2009

### Dreamshot

1. The problem statement, all variables and given/known data

In an experiment to determine the spring constant of an elastic cord of length 0.60 m, a student hangs the cord from a rod as represented above and then attaches a variety of weights to the cord. For each weight, the student allows the weight to hang in equilibrium and then measures the entire length of the cord. The data are recorded
in the table below:
Weight (N) 0 10 15 20 25
Length (m) 0.60 0.97 1.24 1.37 1.64

a) Determine an experimental value for the spring constant k of the cord.

The student now attaches an object of unknown mass m to the cord and holds the object adjacent to the point at
which the top of the cord is tied to the rod, as represented above. When the object is released from rest, it falls
1.5 m before stopping and turning around. Assume that air resistance is negligible.

(b) Calculate the value of the unknown mass m of the object.

(c) i. Calculate how far down the object has fallen at the moment it attains its maximum speed.

ii. Explain why this is the point at which the object has its maximum speed.

iii. Calculate the maximum speed of the object.
2. Relevant equations

In part A I used 1/2kx^2. 10 N = 1/2k(.97)^2. I calculated it out and got k=21.3 N/m. My instructor gave me 2/3 points on this part. Why?

In part B I set Uel equal to U. 1/2kx^2 = mgh. I used 1.5m as x, which was circled on my paper as wrong. What should I have used?

3. The attempt at a solution

2/3 possible points on A, as described above.
2/3 possible points on B, as described above.
0 points on C i
0 points on C ii
0 points on C iii

Thanks for any help!

2. Jan 29, 2009

### nvn

Dreamshot: h = cord initial length (mass initial height) = 0.6 m. In part a, use F = k*x, not spring strain energy. Therefore, 10 N = k*(0.97 m - h). Average all four measured points. In part b, m*g*(h - x4) = 0.5*k*x4^2, where x4 = h - 1.5 m. For part c.i, d = distance fallen = h - x3, where x3 = -m*g/k. For part c.ii, there is a net force downward for any position above this position. For part c.iii, use conservation of energy to solve for the velocity when the mass is at the position stated in part c.i. Thus, m*g*h + 0 + 0 = m*g*x3 + 0.5*m*v3^2 + 0.5*k*x3^2.

Try it again and see if you get correct answers for all five questions now.

3. Jan 29, 2009

### Hootenanny

Staff Emeritus
Do all values of the weight and length give the same value for k?
What does x represent?