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energy conservation question?
A block of mass 0.25 kg can slide over a frictionless horizontal surface. It is attached to a spring whose stiffness constant is k = 16 N/m. The block is pulled 49 cm and let go.
A) at what position is the kinetic energy equal to the potential energy?
I dont know how to interpret this question
1 Answer
- 6 years agoFavorite Answer
The spring force is conservative so you can use the conservation of energy
Kinetic energy of the block + the potential energy in the spring = Some constant to be determined
To find that constant realize that when the block is pulled to its farthest point and held all of the energy is spring potential, no motion so no kinetic energy
0 + 0.5kA^2 = constant, A being the distance you pull the block.
Now you want kinetic energy to equal potential or KE = 0.5kx^2
So in the equation KE + PE = 0.5kA^2 replace KE = 0.5kx^2
0.5kx^2 + 0.5kx^2 = 0.5kA^2
kx^2 = 0.5kA^2
x^2 = A^2/2
x = A/sqrt(2)
x = 0.49/sqrt(2)
x = 0.346 m or 34.6 cm
