Constants NOTE: This problem uses a tolerance o on 1.0 which s smaller han he us
ID: 2036165 • Letter: C
Question
Constants NOTE: This problem uses a tolerance o on 1.0 which s smaller han he usual 2.0%. Be sure o save a numbers n your calculator and use ose saved numbers hen al ula n an ers or nis problem Geena tests new equipment for an outdoor supply company. She has been asked to test a bow string made from a new elastic material; she does so on one of the company's compound bows. The new bow string turns out not to have good properties for archery; nevertheless Geena's data are well-modeled by a simple equation and are thus useful for study by introductory students Geenas data or he amount o force ?necessary o stretc the new bo string by an amount z when he bo st ng s strung on a particular compound o which is valid over the range 0 cmExplanation / Answer
Geena tests a bow string from a new elastic material. Geena's data is necesary for amount of force F.
F (x) = (179) * (1 - e ( -x / (18.0cm)))
Plot an equation from a graph of the model equation:
Step 1: Put the equation in Slope Intercept Form.
Step 2: Graph the y-intercept point (the number in the b position) on the y-axis. ...
Step 3: From the point plotted on the y-axis, use the slope to find your second point. ...
Step 4: Draw your line using the two points you plotted (y-intercept (b) first, slope (m) second.
As the value of x increases the overall value of the Force is constant. The function is a horizontal line to x - axis.
Part M:
An arrow of mass 57.0 grams is fired horizontally from Geena's selected bow. At that instant the arrow is released by the fingers of the archer, the bow is drawn by 59.0 cm . Once the arrow is released by the fingers of the archer, the only significant horizontal force on the arrow is the force on the arrow by the bowstring; you may assume that all vertical forces on the arrow cancel until after the arrow loses contact with the bowstring.
for example:
Now creating an improved estimated value for the work done on the arrow by bowstring the entire time then the arrow was in contact with the string; Adding together the estimated values of work for the first and second halves of that displacement
A varying downward force Fbis applied halfway between the supports by hanging weights or by pulling with a luggage scale. The downward deflection ymat the mid-point is measured with a dial indicator. The measured ymas a function of Fbare shown in Fig. As expected for elastic deformation, the deflection is proportional to the applied force,. The physics that governs the slope ym/Fbis understood within the Euler-Bernoulli beam theory which is valid for small deflections of thin beams under lateral loads. The expected result for the present situation is
To determine the amount of stored energy, we need to know the draw force Fdas a function of the drawn distance s. To measure this we draw the bow in small steps, taking a picture after every step. To reduce parallax, a 200 mm lens at 10 m is used. After some 15 exposures, having reached full draw, this process is reversed, until back to the rest position. Consequently, data are
obtained when drawing the bow (Fin(s)) and when releasing it (Fout(s)).
W ( Work Done ) = Force X Displacement
= 179 (59-57) / 100 = 179 x 2/100
= 358 / 100 = 3.58 Nm = 3.58 J
Part N:
Height (h) = v t - 4.9 t2
0.59 = v t - 4.9 t2
at the start h= 0, 0 = vt - 4.9 t2
also V2 = 2gh = 2 x 9.8 x 0.59
V = 3.4 m/s
Part O:
Work Done = M g H
Acceleration = Sd / V
=0.59 / 3.4
3.58 = 179 x 9.8 x H x 3.4 / 0.59
H = 3.54 x 10 -4 m
x 10 20 30 40 50 60 f(x) 179 179 179 179 179 179