Chapter 6, Problem 6.91P

DATA In a physics lab experiment, one end of a horizontal spring that obeys Hooke’s law is attached to a wall. The spring is compressed 0.400 m, and a block with mass 0.300 kg is attached to it. The spring is then released, and the block moves along a horizontal surface. Electronic sensors measure the speed υ of the block after it has traveled a distance d from its initial position against the compressed spring. The measured values are listed in the table, (a) The data show that the speed υ of the block increases and then decreases as the spring returns to its unstretched length. Explain why this happens, in terms or the work done on the block by the forces that act on it. (b) Use the work-energy theorem to derive an expression for υ² in terms of d. (c) Use a computer graphing program (for example, Excel or Matlab) to graph the data as υ² (vertical axis) versus d (horizontal axis). The equation that you derived in part (b) should show that υ² is a quadratic function of d, so, in your graph, fit the data by a second-order polynomial (quadratic) and have the graphing program display the equation for this trend-line. Use that equation to find the block’s maximum speed υ and the value of d at which this speed occurs, (d) By comparing the equation from the graphing program to the formula you derived in part (b). calculate the force constant k for the spring and the coefficient of kinetic friction for the friction force that the surface exerts on the block.

d (m)	υ (m/s)
0	0
0.05	0.85
0.10	1.11
0.15	1.24
0.25	1.26
0.30	1.14
0.35	0.90
0.40	0.36