Homework 8: Stickman, envious of human cannonballs, has devised the stickman can

Question

Homework 8: Stickman, envious of human cannonballs, has devised the stickman cannonball. He wants to use a spring with a linear rate of 1000N/m to launch himself into the air. The spring has a free length of 10m, and is compressed to a length of 2m at an angle of 45 degrees. Find Stickman's speed once the spring has reached its free length. Stickman, in an attempt to learn from previous mistakes, would like to include the efficiency of the spring (92%) and the effect of his weight (80kg) on the launch speed. Gravity acts down at 10m/sA2. You may treat stickman as a particle. 10m 45° 2m

Explanation / Answer

height at initial position=2*sin(45)=1.4142 m

height at final position=10*sin(45)=7.07 m

let speed at launch be v.

using conservation of energy:

initial potential energy of the spring + initial potential energy of the stickman=final potential energy of the spring + final potential energy of the stickman + final kinetic energy

==>0.5*spring constant*compression^2*efficiency+mass*g*height=0+mass*g*final height+0.5*mass*speed^2

==>0.5*1000*(10-2)^2*0.92+80*10*1.4142=80*10*7.07+0.5*80*v^2

==>40*v^2=0.5*1000*(10-2)^2*0.92+80*10*1.4142-(80*10*7.07)

==>v=24.958 m/s

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