# Conservation of Energy

The conservation of energy is a fundamental principle in physics, asserting that the total energy within an isolated system remains constant over time, regardless of transformations or exchanges between different forms of energy. This principle, first formulated in the 19th century, underpins numerous scientific theories and practical applications, from understanding the behavior of particles at the quantum level to engineering efficient energy systems. Conservation of energy plays a pivotal role in various fields, including mechanics, thermodynamics, and electromagnetism, guiding research efforts to optimize energy utilization and address environmental concerns surrounding energy production and consumption.

- A ball with a mass of #144 g# is projected vertically by a spring loaded contraption. The spring in the contraption has a spring constant of #48 (kg)/s^2# and was compressed by #6/4 m# when the ball was released. How high will the ball go?
- A spring with a constant of #6 (kg)/s^2# is lying on the ground with one end attached to a wall. An object with a mass of #8 kg# and speed of #1 m/s# collides with and compresses the spring until it stops moving. How much will the spring compress?
- A ball with a mass of #500 g# is projected vertically by a spring loaded contraption. The spring in the contraption has a spring constant of #16 (kg)/s^2# and was compressed by #8/5 m# when the ball was released. How high will the ball go?
- A ball with a mass of #300 g# is projected vertically by a spring loaded contraption. The spring in the contraption has a spring constant of #12 (kg)/s^2# and was compressed by #7/6 m# when the ball was released. How high will the ball go?
- A ball with a mass of #480 g# is projected vertically by a spring loaded contraption. The spring in the contraption has a spring constant of #21 (kg)/s^2# and was compressed by #6/5 m# when the ball was released. How high will the ball go?
- A spring with a constant of #4# #kgs^-2# is lying on the ground with one end attached to a wall. An object with a mass of #1# # kg# and speed of #3# # ms^-2# collides with and compresses the spring until it stops moving. How much will the spring compress?
- A ball with a mass of #150 g# is projected vertically by a spring loaded contraption. The spring in the contraption has a spring constant of #15 (kg)/s^2# and was compressed by #7/5 m# when the ball was released. How high will the ball go?
- A spring with a constant of #4 (kg)/s^2# is lying on the ground with one end attached to a wall. An object with a mass of #5 kg# and speed of #5 m/s# collides with and compresses the spring until it stops moving. How much will the spring compress?
- A spring with a constant of #6 (kg)/s^2# is lying on the ground with one end attached to a wall. An object with a mass of #3 kg# and speed of #1 m/s# collides with and compresses the spring until it stops moving. How much will the spring compress?
- A ball with a mass of #144 g# is projected vertically by a spring loaded contraption. The spring in the contraption has a spring constant of #16 (kg)/s^2# and was compressed by #6/4 m# when the ball was released. How high will the ball go?
- A spring with a constant of #12 (kg)/s^2# is lying on the ground with one end attached to a wall. An object with a mass of #6 kg# and speed of #3 m/s# collides with and compresses the spring until it stops moving. How much will the spring compress?
- A force field is described by #<F_x,F_y,F_z> = < xy , xy-x, 2y -zx > #. Is this force field conservative?
- Clarification on universal gravitational potential energy re: planet orbiting a star?
- A ball with a mass of #450 g# is projected vertically by a spring loaded contraption. The spring in the contraption has a spring constant of #12 (kg)/s^2# and was compressed by #4/3 m# when the ball was released. How high will the ball go?
- A ball with a mass of #400 g# is projected vertically by a spring loaded contraption. The spring in the contraption has a spring constant of #64 (kg)/s^2# and was compressed by #3/4 m# when the ball was released. How high will the ball go?
- A spring with a constant of #3 (kg)/s^2# is lying on the ground with one end attached to a wall. An object with a mass of #4 kg# and speed of #6 m/s# collides with and compresses the spring until it stops moving. How much will the spring compress?
- A spring with a constant of #5 (kg)/s^2# is lying on the ground with one end attached to a wall. An object with a mass of #1 kg# and speed of #9 m/s# collides with and compresses the spring until it stops moving. How much will the spring compress?
- How does the law of conservation of energy relate to Hess' law?
- A spring with a constant of #3 (kg)/s^2# is lying on the ground with one end attached to a wall. An object with a mass of #2 kg# and speed of #9 m/s# collides with and compresses the spring until it stops moving. How much will the spring compress?
- A ball with a mass of #150 g# is projected vertically by a spring loaded contraption. The spring in the contraption has a spring constant of #90 (kg)/s^2# and was compressed by #4/3 m# when the ball was released. How high will the ball go?