The total mechanical energy of an object is the sum of its potential energy (U) and it’s kinetic energy (K). In the absence of friction, total energy is conserved. When a popper is launched straight up, the initial U is defined to be a form of elastic potential energy, Us, which converts to kinetic energy, K=(1/2)mv^2, where m is the mass of the popper and v is the muzzle speed of the popper, prior to leaving the ground. When the popper reaches its maximum height, h, the final K is zero and Ug=mgh, where g is the acceleration due to gravity. Conservation of energy gives that the initial K is equal to the final U after the popper has popped and leaves the ground. Using the information given, determine the spring constant (k) of the popper, using mechanical energy (Ei=Ef) Mass: 0.0150kg Initial Height: 1m Measured Distance: 0.020m Final Height: 0.408m Initial Spring Compression: 0.050m Final Spring Compression: 0m Final Velocity: 0m/s I know the correct answer is 69.6, I’m just not sure how to get there.

The total mechanical energy of an object is the sum of its potential energy (U) and it’s kinetic energy (K). In the absence of friction, total energy is conserved. When a popper is launched straight up, the initial U is defined to be a form of elastic potential energy, Us, which converts to kinetic energy, K=(1/2)mv^2, where m is the mass of the popper and v is the muzzle speed of the popper, prior to leaving the ground. When the popper reaches its maximum height, h, the final K is zero and Ug=mgh, where g is the acceleration due to gravity. Conservation of energy gives that the initial K is equal to the final U after the popper has popped and leaves the ground. Using the information given, determine the spring constant (k) of the popper, using mechanical energy (Ei=Ef) Mass: 0.0150kg Initial Height: 1m Measured Distance: 0.020m Final Height: 0.408m Initial Spring Compression: 0.050m Final Spring Compression: 0m Final Velocity: 0m/s I know the correct answer is 69.6, I’m just not sure how to get there.