The following graph shows the energy profile of the elastic band experiment disc

Question

The following graph shows the energy profile of the elastic band experiment discussed in connection with the Energy lecture: A 0.1 smooth projectile is launched horizontally at a velocity of 10.0 m/s using an elastic band catapult capable of delivering energy as described in the graph above. Applying the same assumptions and approximations upon which the text analysis was based. Estimate the minimum extension of the elastic band (in inches) necessary to accomplish this. At what minimum height above the floor (in feet) must the projectile be launched in order to strike the surface at least 25 ft down range from the launch point?

Explanation / Answer

a)

v = 10 m/s = 32.81 ft/s

Energy = 1/2*mv^2 = 1/2*0.1* 32.81^2 = 53.825 lb-ft^2/s^2 = 53.825*12 / 32.2 in-lbf = 20.06 in-lbf

From graph, for y = 20.05, we get extension x = 17 in

b)

H = 1/2*gt^2 or t = (2H/g)^0.5

and R = vt or t = R/v

Thus R/v = (2H/g)^0.5

H = (R/v)^2 *g/2

H = (25/32.81)^2 *32.2/2

H = 9.347 ft

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