Momentum Problem: Kid Pushing Sled on Ice

[JT1000]

Homework Statement

A kid pushes a sled on ice that is smooth, level and essentially frictionless. The kid is 50kg, the sled is 10kg, he pushes the sled hard enough to give it a veloctity of 5m/s. How fast does he end up moving backwards on the ice when letting go of the sled?

Homework Equations

p=mv

The Attempt at a Solution

I did p=mv to find the sleds momentum which is p=(10)(5) for a total of 50m/s. Due to law of conservation of Momentum the boy will have the same momentum correct? Thus leaving me with finding the boys momentum as 50=(50)v and his velocity being 1m/s? Thanks in advance![/B]

 

[Orodruin]

Due to law of conservation of Momentum the boy will have the same momentum correct?

Yes, but in the opposite direction!

for a total of 50m/s

Your units are off. m/s is a unit of velocity, not of momentum.

50=(50)v

Always write out your units or your equations will not make sense. This should be $50~\mbox{kg m/s} = (50~\mbox{kg}) v$.

 

[JT1000]

Yes, but in the opposite direction!

Your units are off. m/s is a unit of velocity, not of momentum.

Always write out your units or your equations will not make sense. This should be $50~\mbox{kg m/s} = (50~\mbox{kg}) v$.

Oh yes i totally spaced the boy is going the opposite direction! Also i didnt mean to add the m/s to the momentum. I apologize for the lack of units it is duly noted for future equations.
50 kg m/s=(50kg)v
Velocity of the boy = 1kg m/s

 

[Orodruin]

Velocity of the boy = 1kg m/s

Again, units.

 

[JT1000]

This is the boys speed in reference to the sled so wouldent the correct unit be 1kg m/s?

 

[Orodruin]

kg m/s is not a unit of speed.

 

[lekh2003]

This is the boys speed in reference to the sled so wouldent the correct unit be 1kg m/s?

Regardless of the boy's speed relative to any object, speed will always me m/s. This is exactly how momentum will always be kg m/s.

Edit: Orodruin beat me to it...

 

[JT1000]

Regardless of the boy's speed relative to any object, speed will always me m/s. This is exactly how momentum will always be kg m/s.

Edit: Orodruin beat me to it...

Ah dangit thank you guys I'm over thinking this one! Been at it for a while and it makes sense now. Thanks so much for your help!

 

[lekh2003]

Ah dangit thank you guys I'm over thinking this one! Been at it for a while and it makes sense now. Thanks so much for your help!

Always happy to help.

 

[lekh2003]

A tip I can give you to avoid these units issues is to work with the units in your equation. Pretend like the units are variables that are always present with their corresponding numbers. This way, you will always end up with the correct units in the end.

 

[JT1000]

A tip I can give you to avoid these units issues is to work with the units in your equation. Pretend like the units are variables that are always present with their corresponding numbers. This way, you will always end up with the correct units in the end.

Ya definietely not a bad idea. I tend to not use them as I work through it but I'll be using them for now on in my work process.

 

[lekh2003]

Ya definietely not a bad idea. I tend to not use them as I work through it but I'll be using them for now on in my work process.

I used to work like you did. I had come to physics right after a few math courses. In those courses, units were basically useless and never bothered about. I thought that units would be too much of a hassle at first, but I came to love the idea.

 

[JT1000]

I used to work like you did. I had come to physics right after a few math courses. In those courses, units were basically useless and never bothered about. I thought that units would be too much of a hassle at first, but I came to love the idea.

Haha much the same, finished up my math courses then got into physics and other sciences but can definietely tell doing it that way will help a ton in the long run.