Finding the Maximum Speed of a Spring-Driven Ball

[omarMihilmy]

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 ?

 

[infinite.curve]

Think about the work energy theorem.

Does that help?

 

[omarMihilmy]

Not really 2 unknowns !
No other equations !

 

[Konoha]

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.

 

[infinite.curve]

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=...

 

[omarMihilmy]

Guys I already solved a) my problem is in b and c where he asks for the point at which velocity is maximum!

 

[infinite.curve]

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?

 

[cepheid]

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

 

[omarMihilmy]

I wrote the complete question in my original post !

 

[omarMihilmy]

B) at what point will the ball have a maximum speed ?

C) what is the maximum speed?

 

[adjacent]

B) at what point will the ball have a maximum speed ?

C) what is the maximum speed?

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

 

[cepheid]

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?

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.

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.