What is the Conservation of Energy Homework Problem?

In summary, the conversation discusses using conservation of energy to solve a problem involving a sphere hanging from a string and swinging through a given angle. The problem involves finding the height and velocity of an arrow shot upwards, using the equation h=\frac{k}{2mg}d^2-d, where k=898N\cdot m, m=0.0907kg, and d=27in. The solution provided calculates the height to be 217.55m, and discusses the order of operations for solving the problem.
  • #1
the whizz
32
0

Homework Statement



attached

Homework Equations



equation in the problem

k = 898 N/m
m = 90.7g = .0907kg
d = 27 inch = .6558m
g = 9.8 m/s

The Attempt at a Solution



h = [(898n/m)/(2)(.0907kg)(9.8m/s)](.6558m)^2 - (.6558)

that is for the H. when computing this is got 217.55m. I am assuming the way the equation is written out for h in the problem that is how to set it up.

now it asks for velocity.

when it gets back to zero. We will say E1 = E2...

at E1 it is all potential energy and no kinetic. and at E2 where we find final velocity it is all kenetic and no potential?



so then we have mgh = 1/2 mv^2...

plus the top equation in for h

then isolate V and solve.

thanks for any help.
 

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  • #2
just curious do most people not like attachments...

Its the best way for me to post the problems because a lot of equations have trouble making readable just typing in.
 
  • #3
Here's his problem:

6.) A sphere of mass [tex]m[/tex] hangs from a string of length [tex]l[/tex] and is drawn back so that the string makes an angle of [tex]\theta[/tex] with the vertical axis. It swings down until the strings hits a peg which is [tex]l/2[/tex] directly below the point where the string is attached to the ceiling. When the string hits the peg, the sphere keeps moving and swings up through an angle [tex]\alpha[/tex]. Use conservation of energy to find an equation for the angle [tex]\alpha[/tex]. Show that this equation makes sense with a few, well-chosen examples for [tex]\theta[/tex].
 
Last edited:
  • #4
sent. ty.
 
  • #5
the whizz said:
sent. ty.

The problem's posted in the above post; if you want, you can "quote" me and select what I typed and put it in the original post. Otherwise, here's my suggestion:

You know the conservation of energy equation:

[tex]U_0+K_0=U+K[/tex], where [tex]U[/tex] indicates potential energy and [tex]K[/tex] represents kinetic energy. What do the two critical moments have for their energy?
 
  • #6
yes i am sorry that one is the wrong question for the work i included...resent you the right one. I will most likely be able to use that one too though so thank you.
 
  • #7
the whizz said:
yes i am sorry that one is the wrong question for the work i included...resent you the right one. I will most likely be able to use that one too though so thank you.

Neglect air resistance.

The height of an arrow shot directly upwards from an inital height [tex]0m[/tex] is given by: [tex]h=\frac{k}{2mg}d^2-d[/tex]. [tex]k=898N\cdot m[/tex], mass is [tex]0.0907kg[/tex], and [tex]d=27in[/tex]; find [tex]h[/tex]. And, find [tex]v[/tex] at [tex]h=0[/tex].
 
  • #8
asleight said:
Neglect air resistance.

The height of an arrow shot directly upwards from an inital height [tex]0m[/tex] is given by: [tex]h=\frac{k}{2mg}d^2-d[/tex]. [tex]k=898N\cdot m[/tex], mass is [tex]0.0907kg[/tex], and [tex]d=27in[/tex]; find [tex]h[/tex]. And, find [tex]v[/tex] at [tex]h=0[/tex].

the whizz said:

Homework Statement



attached

Homework Equations



equation in the problem

k = 898 N/m
m = 90.7g = .0907kg
d = 27 inch = .6558m
g = 9.8 m/s

The Attempt at a Solution



h = [(898n/m)/(2)(.0907kg)(9.8m/s)](.6558m)^2 - (.6558)

that is for the H. when computing this is got 217.55m. I am assuming the way the equation is written out for h in the problem that is how to set it up.

now it asks for velocity.

when it gets back to zero. We will say E1 = E2...

at E1 it is all potential energy and no kinetic. and at E2 where we find final velocity it is all kenetic and no potential?



so then we have mgh = 1/2 mv^2...

plus the top equation in for h

then isolate V and solve.

thanks for any help.

ok put the two together
 
  • #9
the whizz said:
ok put the two together

That sounds perfect.
 
  • #10
asleight said:
Neglect air resistance.

The height of an arrow shot directly upwards from an inital height [tex]0m[/tex] is given by: [tex]h=\frac{k}{2mg}d^2-d[/tex]. [tex]k=898N\cdot m[/tex], mass is [tex]0.0907kg[/tex], and [tex]d=27in[/tex]; find [tex]h[/tex]. And, find [tex]v[/tex] at [tex]h=0[/tex].

the whizz said:

Homework Statement




k = 898 N/m
m = 90.7g = .0907kg
d = 27 inch = .6558m
g = 9.8 m/s

The Attempt at a Solution



h = [(898n/m)/(2)(.0907kg)(9.8m/s)](.6558m)^2 - (.6558)

that is for the H. when computing this is got 217.55m. I just wanted to check on the math here.

we shoulddo k/2mg first then multiply that times d^2 then subtract d. any check on the solution would be great.
 

1. What is the law of conservation of energy?

The law of conservation of energy states that energy cannot be created or destroyed, but can only be transformed from one form to another.

2. Why is conservation of energy important?

Conservation of energy is important because it is a fundamental law of physics that governs all natural processes. It allows us to understand and predict how energy is used and transferred in different systems, and also helps us to develop sustainable energy sources.

3. How is energy conserved in different systems?

In closed systems, energy is conserved through the principle of conservation of mass and energy, which states that the total energy of a system remains constant over time. In open systems, energy can be conserved through processes such as heat transfer, work, and mass flow.

4. Can energy be transformed from one form to another without any loss?

No, according to the law of conservation of energy, energy cannot be created or destroyed, but can only be converted from one form to another. However, some energy transformations may result in the dissipation of energy in the form of heat or other forms of energy loss.

5. How does conservation of energy relate to sustainability?

Conservation of energy is closely related to sustainability because it promotes the efficient use of energy resources and helps to reduce our impact on the environment. By conserving energy, we can reduce our carbon footprint and help to preserve natural resources for future generations.

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