A boy wishes to make a catapult out of a rubber band of width 9mm and thickness 1.55mm. Determine the length of the band that must use so that when he stretches it by 0.25 of its natural length and releases it the velocity of a pebble of mass 0.006kg will be 30m\s. take the young modulus of the rubber to be 4×10^7 N\m^2.?
dosty890
11 Apr, 2023
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Young's modulus = stress/strain = (FL0)/A(Ln − L0). This is a specific form of Hooke's law of elasticity. The units of Young's modulus in the English system are pounds per square inch (psi), and in the metric system newtons per square metre (N/m2).
The equation for change in length is traditionally rearranged and written in the following form: FA=YΔLL0. F A = Y Δ L L 0 . The ratio of force to area, FA , is defined as stress (measured inN/m2 ), and the ratio of the change in length to length, ΔLL0 Δ L L 0 , is defined as strain (a unitless quantity).
young modulus= force(mass x acceleration) x length/area x extension
4 x 10^7 = 6 x 30 x length/9 x1.55 0.25
cross multiply
3.49 x4 x 10^7= 180 x length
13.96 x 10^7=180 x length
DIVIDE BOTH SIDES BY 180
13.96 X 10^7/180= LENGTH
0.07756 X 10^7MM= LENGTH
CONVERT TO METER
LENGTH = 7.8 X 10^2meter
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