Force and Energy
If we ignore damping effects, we can conclude that there are only two forces acting upon the mass vibrating on the vertical spring - - the force of gravity and the spring force. Since the spring is stretched downwards in all three positions, the spring force is directed upwards. The force of gravity is directed downward. Each of these forces are conservative-type forces that serve to change the potential energy into kinetic energy (and vice versa) without changing the total amount of mechanical energy. So if we ignore the effects of friction and air resistance, we can conclude the total mechanical energy (TME) is conserved.
Gravitational Potential Energy
The gravitational potential energy (PEgrav) is the energy stored due to the vertical height of the mass within Earth's gravitational field. As the mass is elevated to higher vertical positions, the gravitational potential energy increases.
When approached quantitatively, a determination of the amount of PEgrav requires that one identify the zero height position. It could be the floor of your second floor classroom, the ceiling, the street level outside your school building, etc. In this activity, it has been picked for you. It is the height of the spring's bottom when in its relaxed state. This is the x = 0 position where x represents the amount of displacement of the spring from its relaxed state. Because the mass on the spring is always located below this height, the PEgrav values are negative. The further below this height, the more negative the PEgrav values will be. Since you are presented negative values for PEgrav, you will have to be extra cautious. Think about it now. An increase in PEgrav means that the PEgrav value will be less negative. The locations with the smallest PEgrav will be those locations that have the most negative values.
Elastic Potential Energy
The elastic potential energy (PEspring) is the energy stored in the mass-spring system due to the amount the spring is stretched or compressed relative to its relaxed state. The amount of elastic potential energy is proportional to the square of the stretch distance. The relaxed state is shown in the first of three snapshots of the spring (far left); it is marked as the x=0 position. The further downward the spring stretches, the more elastic potential energy that will be stored in the system. There will never be a negative value for PEspring. It is calculated as 1/2•kx2. The value of k (the spring constant) is always positive.
Kinetic Energy
The kinetic energy depends upon the speed of the object. As the speed of an object increases, its kinetic energy will increase. The equilibrium position of the mass is shown on the diagram. When the mass located above this position, there is a net downward force upon it. So as it moves upward above equilibrium, the mass will be slowing down. And as the mass moves downward from above equilibrium towards equilibrium, it will be speeding up.
When the mass is located below the equilibrium position, there is a net upward force acting upon it. So as the mass moves downward from equilibrium towards its lowest, most extreme position, it will be slowing down. And as the mass moves upward from its lowest position towards equilibrium, it will be speeding up.
Your Best Approach
Your best approach is know the above principles and use them to rule out options from among the three options. Ask questions like ...
- Do any options shown an increase or decrease in total energy? If so, then rule out the option.
- Do any options show an increase in elastic PE (PEspring) when it should be decreasing (or vice versa)? If so, then rule out the option.
- Do any options show an increase in gravitational PE (PEgrav) when it should be decreasing (or vice versa)? If so, then rule out the option.
- Do any options show an increase in kinetic energy (KE) when it should be decreasing (or vice versa)? If so, then rule out the option.
By ruling out options there will often be only one remaining option that is reasonable. Tap on it and collect your Dataway!