# Question Solved1 AnswerA particle of mass $$\frac{1}{2} \mathrm{~kg}$$ is attached to one end of a model spring which is hanging vertically from a fixed point $$A$$. The spring has stiffness $$4 \mathrm{Nm}^{-1}$$ and a natural length of 1 metre. The system is oscillating in a vertical line with the particle below $$A$$. Use the approximation that the magnitude of the acceleration due to gravity is $$10 \mathrm{~ms}^{-2}$$. (a) Find an expression for the total mechanical energy function for the system, carefully defining your coordinate system and the datum for gravitational potential energy. (b) When the particle is 2 metres below $$A$$ it has speed $$2 \mathrm{~ms}^{-1}$$. Use conservation of mechanical energy to establish whether the spring is ever in compression during the motion. (Hint: try to determine the speed of the particle when the spring has its natural length.)

Transcribed Image Text: A particle of mass $$\frac{1}{2} \mathrm{~kg}$$ is attached to one end of a model spring which is hanging vertically from a fixed point $$A$$. The spring has stiffness $$4 \mathrm{Nm}^{-1}$$ and a natural length of 1 metre. The system is oscillating in a vertical line with the particle below $$A$$. Use the approximation that the magnitude of the acceleration due to gravity is $$10 \mathrm{~ms}^{-2}$$. (a) Find an expression for the total mechanical energy function for the system, carefully defining your coordinate system and the datum for gravitational potential energy. (b) When the particle is 2 metres below $$A$$ it has speed $$2 \mathrm{~ms}^{-1}$$. Use conservation of mechanical energy to establish whether the spring is ever in compression during the motion. (Hint: try to determine the speed of the particle when the spring has its natural length.)
Transcribed Image Text: A particle of mass $$\frac{1}{2} \mathrm{~kg}$$ is attached to one end of a model spring which is hanging vertically from a fixed point $$A$$. The spring has stiffness $$4 \mathrm{Nm}^{-1}$$ and a natural length of 1 metre. The system is oscillating in a vertical line with the particle below $$A$$. Use the approximation that the magnitude of the acceleration due to gravity is $$10 \mathrm{~ms}^{-2}$$. (a) Find an expression for the total mechanical energy function for the system, carefully defining your coordinate system and the datum for gravitational potential energy. (b) When the particle is 2 metres below $$A$$ it has speed $$2 \mathrm{~ms}^{-1}$$. Use conservation of mechanical energy to establish whether the spring is ever in compression during the motion. (Hint: try to determine the speed of the particle when the spring has its natural length.)