1220 \\/ Name: Dale: Objective: To nd the spring constants for three springs. and to predict the period of several mass-spring sys'rems. "T .u 86%- Period Mass On Spring Online PHYS162 - Saw Data Tables Part 1: Spring Constants: A/CPJPI") Physics Laboratory Period of a Mass 011 a Spring Spring [D x1 Part 2: Mass on a Single Spring Spring 1]) in TM l[1l Cycles) NEAR) "In Diff Part 3: Mass on Two Springs in Parallel Spring 1 1D Spring 2 [D k1 kw: TM t (10 cycles) NW!) % Diff Part 4: Mass on Two Springs in Series Spiing 1 1D Spring 2 ID k1 1% TM t (10 cycles) New) % Diff Part 5: Mass on Three Springs in Series and Parallel :priug Spring 2 1 ID ID Spring 3 in ID k] k: ks WK 1' :00 (web cycles) T (we) \"1:, Diff Calculations: Sources of Error: Answer (0 Que stion' Conclusion: The Period of a Mass on a Spring Instructions Notes on Doing and Reporting Labs in General: Read about doing labs in general in \"Introduction to Physics Lab\" in the Lab Information module. Read about the lab report format, also in in Lab Information module. Print or copy the data table for the lab before starting the lab. This is available in the same page as the Lab instructions. An excel version of this data table is also available. Take all measurements and write results in the table. Then when you do the report, you can copy the information into it For This Lab: Objective: To nd the spring constants for three springs, and to predict the period of several mass-spring systems. Materials: the timer of a cell phone, or another timer. Theory; Hooke's Law can written as F. = -kx. where FS is the force by the spring when it is stretched or compressed. The negative sign indicates that this is a restoring force. always in a direction opposite the displacement x. The spring constant k of a spring is a number that tells us how stiff or strong a spring is: in other words. how much force is required to stretch it by a certain distance. The equation F. = -kx shows us that a larger k means it takes a larger force to stretch or compress a spring by a certain distance x. The expression for the period of a mass on a single spring is T=2rr'i% where T = period. m = mass attached to the spring. and k = spring constant. The derivation of this equation is found in your textbook (Chapter 15. equation 15.3). The period T is the time for one complete back-and-forth motion. The difference between two results can be expressed as Percent Difference. See the Lab Information module for how to calculate this. Procedure: 1. We will stretch a spring by hanging a known mass (weight) on the spring. The upward force by the spring is F = kx. The weight ofthe hanging object is downward Fg = -mg. The forces balance each other: 2 F = k2: mg = 0 and: k = mgfx. Instead of writing a negative number for mg and a negative number for x, we can simply consider both to be positive. k is always a positive number. 2. A spring without any stretch does not give us a good zero point to measure from - the windings are pressed up against each other - so we will use two different forces producing two different stretches. If one force. F1. produces a stretch x1, then F1 = -kx1. Likewise. for a second force. F2 = 40:2. Subtracting these two equations yields F2'F1 = -k(x2-x1), or AF = -k Ax. AF is the difference between the forces: this becomes Amg. Ax is the difference in positions. So our equation becomes k = Amgi'Ax Be sure to use SI units (kg. m. s) for your measurements and results. 3. We will work with three different springs: We will label them short, medium and long. To set some basic values. we can use a scale to nd the mass of a mass hanger [on which we will place other masses) and the actual mass of the 100 g and 50 g masses. Here are photos of that operation:: 2:30 an... 66%- X 5 The Period of a M...