Question

javier martinez, star rodriguez, kaleb, h dominic. mass in kg gram/1000 = kg weight applied by the mass = m*9.8 stretch in meters = cm/100 k value k = f/δx average spring constant 0.0106 kg = 1 disc 0.10388 n 0.01 10.388 9.165 0.0212 kg = 2 discs 0.20776 n 0.022 9.44364 0.0318 kg = 3 discs 0.31164 n 0.035 8.904 0.0424 kg = 4 discs 0.41552 n 0.048 8.65 0.0530 kg = 5 discs 0.51944 n 0.06 8.45 - your k - values should be relatively (10% rule) consistent, because the spring constant should be the same, as long as you dont change the spring! 1. calculations for spring constant for any one of your trials, must complete calculations for all trials, but only show work for any one. 2. now hang the unknown mass and measure its stretch. use the spring force formula to solve for the weight of the object, then solve for mass. (you must get an unknown mass from me.) 3. draw the fbd of the unknown hanging mass when it is stationary, hanging on the spring.

Explanation:

Step1: Recall Hooke's Law formula

$F = kx$, where $F$ is the force applied, $k$ is the spring - constant and $x$ is the displacement. We can re - arrange it to find $k=\frac{F}{x}$.

Step2: Choose a trial for calculation

Let's take the first trial: $F = 0.10388N$ and $x = 0.01m$.

Step3: Calculate the spring - constant

$k=\frac{F}{x}=\frac{0.10388N}{0.01m}=10.388N/m$

For the second part (finding mass of unknown object), assume the stretch of the spring when the unknown mass is hung is $x_{unknown}$ and we know from Hooke's Law $F = kx_{unknown}$, and since $F = mg$, then $m=\frac{kx_{unknown}}{g}$. But we need the value of $x_{unknown}$.

For the third part (drawing FBD):

• The forces acting on the stationary hanging mass are the force of gravity $F_g=mg$ acting downwards and the spring force $F_s = kx$ acting upwards. We draw a dot to represent the mass, an arrow pointing downwards labeled $mg$ and an arrow pointing upwards labeled $kx$.

Answer:

1. For the first trial, the spring - constant $k = 10.388N/m$.
2. Mass of unknown object $m=\frac{kx_{unknown}}{g}$ (need value of $x_{unknown}$).
3. FBD: A dot representing the mass with a downward - pointing arrow labeled $mg$ and an upward - pointing arrow labeled $kx$.