Using Energy Conservation to solve this problem: Jumping on a spring scale

In summary, the conversation discussed the use of algebra to solve for spring compression and potential energy. The solution manual made a typing error in stating that 760=0.5kX²+760X instead of 760=0.5kX²-760X, indicating a negative value for X. Further testing was not possible due to limited equipment capabilities.
  • #1
r12214001
24
2
Homework Statement
my cal:760(1+X)=0.5kX²
Relevant Equations
760(1+X)=0.5kX²
I suppose spring compression to be X when jumpping from 1m. Therefore gravational potential mgh=760(1+X) and my cal:760(1+X)=0.5kX²
why the solution manual state that 760=0.5kX²+760X

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  • #2
r12214001 said:
I suppose spring compression to be X when jumpping from 1m. Therefore gravational potential mgh=760(1+X) and my cal:760(1+X)=0.5kX²
why the solution manual state that 760=0.5kX²-760X
Algebra.

Start with$$760(1+X)=0.5kX^2$$ and subtract ##760X## from both sides to get $$760(1+X)-760X=0.5kX^2-760X$$Now on the left hand side notice that you can cancel that 760X and get $$760=0.5kX^2-760X$$
 
  • #3
jbriggs444 said:
Algebra.

Start with$$760(1+X)=0.5kX^2$$ and subtract ##760X## from both sides to get $$760(1+X)-760X=0.5kX^2-760X$$Now on the left hand side notice that you can cancel that 760X and get $$760=0.5kX^2-760X$$
typing error
solution manual state that 760=0.5kX²+760X
 
  • #4
r12214001 said:
typing error
solution manual state that 760=0.5kX²+760X
The solution manual took ##X## to be negative.
 
  • #5
PS my bathroom scales only go up to about ##150kg## or ##1,500N##. I'm not able to test this out.
 
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  • #6
PeroK said:
PS my bathroom scales only go up to about ##150kg## or ##1,500N##. I'm not able to test this out.
OK i didnt notice that. thanks for correction
 

1. How does jumping on a spring scale relate to energy conservation?

Jumping on a spring scale involves transferring kinetic energy from your body to the scale. This energy is then stored in the spring, causing it to compress. According to the law of conservation of energy, energy cannot be created or destroyed, only transferred or converted. Therefore, the energy you use to jump on the scale is conserved and can be measured by the amount of compression in the spring.

2. Can energy conservation be used to solve the problem of jumping on a spring scale?

Yes, energy conservation can be used to solve this problem. By measuring the amount of compression in the spring, we can calculate the amount of kinetic energy that was transferred from your body to the scale. This can help us determine your weight or the force of your jump.

3. How can energy conservation help us understand the physics behind jumping on a spring scale?

Energy conservation helps us understand the physics behind jumping on a spring scale by showing us how energy is transferred and stored in the spring. It also allows us to make calculations and predictions based on the amount of energy involved in the process.

4. Are there any limitations to using energy conservation to solve this problem?

One limitation of using energy conservation to solve this problem is that it assumes all of the energy is transferred to the spring. In reality, some energy may be lost due to factors such as friction or air resistance. Additionally, the accuracy of the measurements may be affected by the precision of the scale and the consistency of the jumping motion.

5. How can we apply the concept of energy conservation to other everyday activities?

Energy conservation can be applied to many everyday activities, such as riding a bike, throwing a ball, or even cooking. By understanding how energy is transferred and conserved in these activities, we can make informed decisions about how to use energy more efficiently and sustainably.

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