Easy Energy Conservation Problem causing me trouble

In summary, the problem involves finding the speed of a 3.30kg block dropped from a height of 5.70m onto a spring with spring constant 3806 N/m. When the block is momentarily at rest, the spring has compressed by 32.0cm. The approach is to calculate the elastic energy at 32.0cm and subtract it from the elastic energy at 13.5cm to find the remaining potential energy, which is then used to determine the velocity using the kinetic energy equation. However, it is important to also consider the gravitational potential energy in the calculations. Once this is taken into account, the correct answer can be obtained.
  • #1
motoxkx
3
0
Problem:
A 3.30kg block is dropped from a height of 5.70m onto a spring of spring constant 3806 N/m. When the block is momentarily at rest, the spring has compressed by 32.0 cm. Find the speed of the block when the compression of the spring is 13.5cm.

How I approached it:
Calculate the the elastic energy when the spring is compressed 32.0cm. Then subtract the elastic energy when the spring is compressed 13.5cm. Then that energy would be the current kinetic energy, and I determined velocity from that. However, this is not giving me the correct answer.

Calculations:
Elastic Energy at 32.0cm
E = .5kx^2 = .5*3806*.32^2 = 194.8672 J

Elastic Energy at 13.5cm
E = .5kx^2 = .5*3806*.135^2 = 34.682 J

Subtract the potential energy remaining
194.8672 - 34.682 = 160.185 J

Find velocity
Ke = .5mv^2
160.185 = .5*3.30*v^2
v = 9.85 m/s

Where am I going wrong? Thanks in advance
 
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  • #2
motoxkx said:
How I approached it:
Calculate the the elastic energy when the spring is compressed 32.0cm. Then subtract the elastic energy when the spring is compressed 13.5cm. Then that energy would be the current kinetic energy, and I determined velocity from that. However, this is not giving me the correct answer.
Don't forget to include gravitational PE in your energy calculations.
 
  • #3
Doesn't all of the gravitational potential energy become elastic potential energy when the spring is compressed 25 cm?
 
  • #4
Ah, never mind to my last post, I see where the potential energy comes into play because not all of the elastic energy is converted into kenitic energy, and some becomes potential energy. Thank you for the help.
 

Related to Easy Energy Conservation Problem causing me trouble

1. What is easy energy conservation?

Easy energy conservation refers to simple actions that can be taken to reduce energy consumption and save resources. These actions can include turning off lights and electronics when not in use, unplugging chargers and appliances when not in use, and using energy-efficient products.

2. Why is easy energy conservation important?

Conserving energy is important for several reasons. It helps reduce our carbon footprint, which slows down climate change. It also helps save money on utility bills and decreases our dependence on non-renewable energy sources. Additionally, conserving energy can help protect natural resources and improve air quality.

3. What are some common energy conservation problems?

Some common energy conservation problems include forgetting to turn off lights or electronics when leaving a room, not using energy-efficient products, and using appliances or electronics that are old and inefficient. These problems can lead to higher energy bills and unnecessary energy consumption.

4. How can I easily conserve energy at home?

There are many simple ways to conserve energy at home, including turning off lights and electronics when not in use, using energy-efficient light bulbs and appliances, unplugging chargers and appliances when not in use, and adjusting the thermostat to save energy. It's also important to properly maintain and clean appliances to ensure they are running efficiently.

5. How can I encourage others to conserve energy?

One way to encourage others to conserve energy is by setting a good example. Practice energy-saving habits at home and share your knowledge and tips with others. You can also get involved in community initiatives or education programs that promote energy conservation. Additionally, you can advocate for energy-efficient policies and encourage others to do the same.

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