Q. A rubber cord catapult has cross-sectional area 25mm2 and initial length of rubber cord is 10cm. It is stretched to 5cm. and then released to project a missile of mass 5gm. Taking Yrubber = 5 x 108 N/m2, find the velocity of the projected missile.
Please explain your answer. [1]
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5 Answers
62this question is quite simple I think...
assuming that the contact between the catapult rubber and the stone is lost at the end..
you have to apply stress/ strain = Y
then stress = F/A
A is on the average a constant (Another wrong assumption but I am sure the questin uses this assumption)
Now you will be able to find F (for different values of Strain... thus for different extensions)
Now simply use F=ma..
integrate both sides (since F is a function of extension)
To get final velocity...
30Thank you sir.
I got the answer by another method.
The elastic potential energy of the rubber cord catapult finally gets converted into the kinetic energy of the stone.
EPE = 1/2 x F x Δl
Now,
F = YAΔl/l
= 5 x 10-8 x 25 x 10-6 x 5 / 10
= (25)2 x 10
1/2 x F x Δl = 1/2 x m x v2
(25)2 x 10 x 5 x 10-2 = 5 x 10-3 x v2
v= 250 m/s
62@Asish.. are these two different methods? ;)
Think of why not :D
I was thinking of posting this one too.. but thought you would figure out that they are one and the same :P