Finding the Maximum Speed of a Spring-Driven Ball

In summary, the conversation involves a question about finding the point at which a ball will have maximum speed. The person asking for help has attempted to conceptualize an answer, but the provided answers disagree with their approach. The other person suggests using the work energy theorem to solve the problem and clarifies that the ball's maximum speed will be when it just leaves the toy without moving any of the 15cm of the cannon. The conversation also includes a discussion about posting homework help threads on a forum and the importance of including an exact problem statement and an attempt at the solution.
  • #1
omarMihilmy
31
0
ImageUploadedByPhysics Forums1387563483.653939.jpg


The rest if the question ask me to find the the point at which the ball will have maximum speed ?

I don't know how to approach it exactly?
From my conceptualization I can see that the maximum will be when the spring returns to the uncompressed position at 5.0cm. However the answers disagree and they claim its 4.6 cm ?

Please help me how did he reach this conclusion ?
 
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  • #2
Think about the work energy theorem.

Does that help?
 
  • #3
Not really 2 unknowns !
No other equations !
ImageUploadedByPhysics Forums1387566332.576675.jpg
 
  • #4
You actually know x here. as it says in the problem: "the ball moves 15 cm through the barrel of the canon and the barrel exerts a constant friction force of 0.032N on the ball". This 15 cm is where the friction is doing work.
 
  • #5
Man... My picture did not upload. Anyone else has this problem?

Yes! Now you would get... -0.320x0.15=1/2x5.30x10^-3kgV^2-1/2x8x0.05^2

Now... V=...
 
  • #6
Guys I already solved a) my problem is in b and c where he asks for the point at which velocity is maximum!
 
  • #7
omarMihilmy said:
Guys I already solved a) my problem is in b and c where he asks for the point at which velocity is maximum!

Can you please be more specific about what b & c are?

Is it when compression m(-x+500) is at a distance x?
 
  • #8
omarMihilmy said:
Guys I already solved a) my problem is in b and c where he asks for the point at which velocity is maximum!

It would help if you had actually posted parts b and c of the problem, then :rolleyes:
 
  • #9
I wrote the complete question in my original post !
 
  • #10
B) at what point will the ball have a maximum speed ?

C) what is the maximum speed?
 
  • #11
omarMihilmy said:
B) at what point will the ball have a maximum speed ?

C) what is the maximum speed?
omarMihilmy said:
B) at what point will the ball have a maximum speed ?

C) what is the maximum speed?
The ball would have the maximum speed when it just leaves from the toy,without moving any of the 15cm of the cannon.

Using F=ma and F=ke --> k=Force constant e =extension
Find force.
Using F=ma,Find acceleration
Then you can know the speed
 
  • #12
omarMihilmy said:
I wrote the complete question in my original post !

Don't give me your indignation, man. You were supposed to use the template for posting homework help threads, the one that requires an *exact* problem statement and an attempt at the solution. You know, the template that you deleted when you made your original post, in spite of being asked in boldface red text to use it? Didn't you see this above the compose window?

attachment.php?attachmentid=64978&stc=1&d=1387600631.png


So your post is in violation of PF rules, and by all rights I should delete it. But I'll let you off this time.


omarMihilmy said:
View attachment 64963

I don't know how to approach it exactly?
From my conceptualization I can see that the maximum will be when the spring returns to the uncompressed position at 5.0cm. However the answers disagree and they claim its 4.6 cm ?

The above would be true if there were no friction. But there is friction, which does work, removing kinetic energy from the system. So your expression for the conservation of energy must include the work done by friction. If you write down the conservation of energy in this way, you will end up for an expression for the kinetic energy vs. position. From that, it shouldn't be too hard to solve for the position that maximizes the kinetic energy.
 

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1. What is the definition of work in the context of spring work and energy?

The scientific definition of work is the product of force and displacement in the direction of the force. In the context of spring work and energy, work is the force applied to compress or stretch a spring, resulting in potential energy stored within the spring.

2. How is the potential energy of a spring calculated?

The potential energy of a spring can be calculated using the equation PE = 1/2kx², where PE is potential energy, k is the spring constant, and x is the displacement of the spring from its equilibrium position.

3. What is the relationship between the spring constant and the stiffness of a spring?

The spring constant, represented by the letter k, is a measure of the stiffness of a spring. A higher spring constant means that the spring is stiffer, while a lower spring constant indicates a more flexible spring.

4. How does Hooke's Law relate to spring work and energy?

Hooke's Law states that the force applied to a spring is directly proportional to the displacement of the spring from its equilibrium position. This relationship is important in understanding the work and energy involved in compressing or stretching a spring.

5. Can the potential energy of a spring be converted into other forms of energy?

Yes, the potential energy stored in a spring can be converted into kinetic energy when the spring is released and returns to its equilibrium position. This conversion of energy can be seen in various applications such as trampolines, pogo sticks, and catapults.

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