The Great Sandini is a 60 circus performer who is short from a cannon (actually

Question

The Great Sandini is a 60 circus performer who is short from a cannon (actually a spring gun) you don't find many men of his, so you help him design a new gun. This new gun has a very large spring with a very small mass and a force constant of 1400 that he will compress with a force of 4200 N. The inside of the gun barrel is with so the average friction force will be only 30 N during the distance of 3.0 that he moves in the barrel. Part A At what speed will he emerge from the end of the carrel, a distance 1.1 above his initial rest position?

Explanation / Answer

m= mass = 60 kg

k= force constant = 1400 N/m

F= applied force = 4200 N

f = friction force = 30 N

barrel length = L= 3m

A) V= speed = ?

h= height = 1.1 m

let x be the distance by which spring get compressed.

from F= kx

x = F/ k = 4200 / 1400 = 3m ( which is equal to L ,the entire barrel length)

Since he shot out so,

kinetic energy +gravitational potential energy = elastic energy of the spring - the energy lost due to friction ( = force(f)*distance (L))

K.E + P.E(gravity) = P.E(spring) - E(friction)

(1/2)* mV2 + mgh = (1/2)* k*x2 - f*L

(1/2)*60*V2 + 60*9.8*1.1 = (1/2)*1400*32 - 30*3

V= 13.61 m/s

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