Answer:
a) The initial elastic potential energy of the block-spring system is 28.113 joules.
b) The final speed of the block is approximately 4.192 meters per second.
Explanation:
a) By applying Hooke's law and definition of work, we define the elastic potential energy (), measured in joules, by the following formula:
(1)
Where:
- Spring constant, measured in newtons per meter.
- Deformation of the spring, measured in meters.
If we know that and
, then the elastic potential energy is:
The initial elastic potential energy of the block-spring system is 28.113 joules.
b) According to the Principle of Energy Conservation, the initial elastic potential energy of the block-spring system becomes into translational kinetic energy, that is:
(2)
Where:
- Mass, measured in kilograms.
- Final speed, measured in meters per second.
Then, the final speed is cleared:
If we know that and
, then the final speed of the block is:
The final speed of the block is approximately 4.192 meters per second.