contrast between using a compound bow and using a regular bow is that the force
ID: 1781434 • Letter: C
Question
contrast between using a compound bow and using a regular bow is that the force required to pull the string is lower in the com required to pull a regular bow vs a compound bow (straight line for the regular bow). F(N) 400 pou nd bow. The figure shows the force 200 100 0.15 0.3 0.45 0.6 (I) (10 points) Find the effective force constant for the regular bow (how much force per unit of length). (1) (10 points) Find the work required to draw each of the bows a distance of 0.30m. (One answer per bow). (III) (10 points) Find the work required to draw each of the bows a distance of 0.60m. (One answer per bow).Explanation / Answer
I) From the figure the force required to stretch the bow is continuously increases in case of regular bow.
so we can write F = k.x ; k is effective force constant.
The amount of force required to stretch the bow upto x= 0.6 m is 350 N.
Effective force constant k = F/x = 350 / 0.6 = 583.33 N/m;
II) For regular bow force required to stretch the bow by 0.3 m is F = k * 0.3 = 583.33 * 0.3 = 175 N.
Now the work done W = F.x = 175 * 0.3 = 52.5 Joule.
For combined bow from the plot it is clear that amount of force required to strech the bow by 0.3 m is 200 N.
So work done will be -
W = F.x = 200 * 0.3 = 60 Joule.
III) For regular bow F = k.x = 583.33 * 0.6 = 350 N.
W = 350 * 0.6 = 210 Joule.
For combined bow F = 200 N. (from plot)
W = 200 * 0.6 = 120 Joule.
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