Energy changes of a stretched string

In summary, the conversation discusses the relationship between stretching/extension, force, velocity, and height in regards to Hooke's Law and the principle of conservation of energy. It is determined that as extension is reduced, force also reduces, causing a gain in kinetic energy and a loss in gravitational potential energy, leading to an increase in velocity and height. It is also mentioned that acceleration is always positive until before a certain point, and that height increases because of the upwards acceleration. The mark scheme also states that the height increases, with the main reason being the upwards acceleration.
  • #1
Janiceleong26
276
4

Homework Statement


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This is the answer :

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For part d) of this question, I don't understand "stretching/extension reduces and velocity increases/height increases" .

Homework Equations


Hooke's Law: F=kx

The Attempt at a Solution


Ok, so if extension is reduce, then force reduces too. Then how does a decrease in force causes the velocity and height to increase? Does it have something to do with the principle of conservation of energy, where a gain in kinetic energy equals to a lose in gravitational potential energy?
 
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  • #2
At a point lower than R , how does spring force compare to force of gravity ?
 
  • #3
Qwertywerty said:
At a point lower than R , how does spring force compare to force of gravity ?

Spring force is more than the force of gravity .
 
  • #4
Janiceleong26 said:
Spring force is more than the force of gravity .
So as long as mass is below R , acceleration is ( +ve or -ve ) ? And therefore velocity will always what ?
 
  • #5
Qwertywerty said:
So as long as mass is below R , acceleration is ( +ve or -ve ) ? And therefore velocity will always what ?

Positive..? I'm not sure.. Therefore, velocity will increase?
 
  • #6
Janiceleong26 said:
Positive..? I'm not sure.. Therefore, velocity will increase?
Yes . ( kx - mg = ma ) , kx > mg .

Now , a = dv/dt . As a is always positive till before R , dv is always +ve , and hence velocity will increase till R .

Hope this helps .
 
  • #7
Qwertywerty said:
Yes . ( kx - mg = ma ) , kx > mg .

Now , a = dv/dt . As a is always positive till before R , dv is always +ve , and hence velocity will increase till R .

Hope this helps .

But how do you know that a is always +ve till before R? And why height increases? Does it got to do with 1/2 mv^2=mgh (gain in kinetic energy=lost in gravitational potential energy) ? And thanks by the way. :)
 
  • #8
Janiceleong26 said:
But how do you know that the a is always +ve till before R?
I thought we agreed that -
Qwertywerty said:
( kx - mg = ma ) , kx > mg .
Janiceleong26 said:
And why height increases?
It rises because acceleration is upwards . And that's pretty much the only reason .
 
  • #9
Qwertywerty said:
I thought we agreed that -It rises because acceleration is upwards . And that's pretty much the only reason .

Yeah, I agreed to that one. But the mark scheme also states that the height increases as well. Why?
 
  • #10
Janiceleong26 said:
Yeah, I agreed to that one. But the mark scheme also states that the height increases as well. Why?
Qwertywerty said:
It rises because acceleration is upwards . And that's pretty much the only reason .
 
  • Like
Likes Janiceleong26
  • #11
OK thanks
 

FAQ: Energy changes of a stretched string

How does the tension affect the energy of a stretched string?

The tension of a stretched string directly affects its energy. As the tension increases, so does the energy stored in the string. This is because the tension causes the string to stretch, and the more it stretches, the more potential energy it has.

What happens to the energy of a stretched string when it is released?

When a stretched string is released, the energy stored in it is converted into kinetic energy as the string vibrates back and forth. This is why we can hear sound from a plucked or bowed string - the energy of the string's vibration is transferred into the air as sound waves.

How does the length of a stretched string affect its energy?

The length of a stretched string also affects its energy. The longer the string, the more potential energy it can store when stretched. This is because a longer string has more room to stretch and therefore can store more energy.

Does the material of the string impact its energy changes?

Yes, the material of the string does impact its energy changes. Different materials have different levels of elasticity, which affects how much the string can stretch and therefore how much energy it can store. For example, a steel guitar string will have a higher energy storage capacity than a nylon string due to its higher elasticity.

How does temperature affect the energy of a stretched string?

Temperature can also impact the energy changes of a stretched string. As temperature increases, the molecules in the string begin to vibrate more, causing the string to expand and decrease in tension. This results in a decrease in the energy stored in the string. Conversely, a decrease in temperature will cause the string to contract and increase in tension, increasing the energy stored in the string.

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