To launch a 60 kg human at the given speed, the spring constant needed is 1500 N/m.
<h3>What is spring constant?</h3>
This is the proportion of a spring's extension to the force applied to it. Utilizing the energy conservation principle, the spring's spring constant is determined. The human will transform the elastic potential energy of the spring into kinetic energy in order to launch at the desired speed.
<h3>Briefing:</h3>
U = K.E
¹/₂kx² = ¹/₂mv²
k = mv²/x²
where;
m is mass of the human
v is the speed of the cannon
x is the extension of the spring
k is the spring constant
Substitute the given parameters and solve for the spring constant.
k = (60x 15²) / (3²)
k = 1500 N/m
A spring constant of 1500 N/m is need to maintain the law of conservation of energy, from elastic potential energy of the spring to kinetic energy of the human,
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The complete question is -
In order To launch a 60 kg human so that he leaves a cannon moving at a speed of 15 m/s, you need a spring with an appropriate spring constant. This spring will be compressed 3.0 m from its natural length to launch the person. The cannon oriented at an angle of 37⁰ above the horizontal?
a) Which spring constant should the spring have so that the cannon functions as desired?
