Calculating Energy Conservation in a Spring-Mass System

In summary, the conversation is discussing the total energy of a system consisting of a ball, spring, and earth. The total energy at a specific point is calculated by adding the elastic potential energy (1/2 kx^2) and the gravitational potential energy (mgh). The total energy at a later point, assuming energy conservation, would be equal to the kinetic energy (1/2 mVx^2). This is because the spring potential energy is transformed into kinetic energy. The final point would also take into account the constant horizontal velocity of the ball under projectile motion.
  • #1
Pseudo Statistic
391
6
In the attached picture below I am compressing a spring...
In picture 2, I've compressed the spring a distance x and thus the elastic potential is 1/2 kx^2 and the total energy in the system AT THAT POINT is 1/2 kx^2 + mgh, isn't it? (m is the mass of the ball and h the height from my reference level, the floor) Or am I wrong in thinking this?
Assuming energy conservation, let's say I let go of the spring and it's at that point where it has JUST gone over the edge of the table with its constant horizontal velocity Vx; would the total energy at that point be equal to 1/2 mVx^2 (where m is the mass of the ball) or would I be wrong in assuming this?
Thanks for any help.
 

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  • #2
Pseudo Statistic said:
In the attached picture below I am compressing a spring...
In picture 2, I've compressed the spring a distance x and thus the elastic potential is 1/2 kx^2 and the total energy in the system AT THAT POINT is 1/2 kx^2 + mgh, isn't it? (m is the mass of the ball and h the height from my reference level, the floor) Or am I wrong in thinking this?
Your thinking seems correct. That would be the total mechanical energy of the ball/spring/earth system.

Assuming energy conservation, let's say I let go of the spring and it's at that point where it has JUST gone over the edge of the table with its constant horizontal velocity Vx; would the total energy at that point be equal to 1/2 mVx^2 (where m is the mass of the ball) or would I be wrong in assuming this?
You forgot the gravitational PE (mgh). The total mechanical energy at that point would be its KE + mgh.
 
  • #3
Alright so, the mghs in the equality would cancel out leaving us with 1/2mv^2 = 1/2 kx^2, wouldn't it?
Thanks for the reply.
 
  • #4
That's right. The spring PE is transformed into KE. (Since the height never changes, the gravitational PE remains constant.)
 
  • #5
Alright, thanks, but one more thing...
The kinetic energy would be equal to half of the mass times by the constant horizontal velocity the ball would experience when under projectile motion squared, correct?
 

Related to Calculating Energy Conservation in a Spring-Mass System

What is energy conservation?

Energy conservation is the practice of reducing the amount of energy used in a system or process. This can include using energy-efficient technology, changing behaviors and habits, and finding alternative sources of energy.

Why is energy conservation important?

Energy conservation is important for several reasons. First, it helps to reduce our carbon footprint and combat climate change. Second, it can save money on energy bills. Third, it helps to preserve natural resources for future generations.

What are some ways to conserve energy?

There are many ways to conserve energy, including turning off lights and electronics when not in use, using energy-efficient appliances, adjusting thermostats to reduce heating and cooling, using public transportation or carpooling, and using renewable energy sources.

How does energy conservation benefit the environment?

Energy conservation benefits the environment by reducing greenhouse gas emissions, which contribute to climate change. It also helps to preserve natural resources, such as fossil fuels, that are used to produce energy. Conserving energy also helps to protect ecosystems and wildlife that may be affected by energy production and consumption.

What role can individuals play in energy conservation?

Individuals can play a significant role in energy conservation by being mindful of their energy use and making small changes in their daily habits. This can include turning off lights and electronics when not in use, using public transportation or biking instead of driving, and choosing energy-efficient appliances and products. Individuals can also advocate for policies and initiatives that promote energy conservation on a larger scale.

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