How do momentum and center of mass play a role in solving a boat problem?

[haydn]

Homework Statement

Homework Equations

p=mv
X_CM = (m₁x₁ + m₂x₂)/(m₁ + m₂)

The Attempt at a Solution

I'm really confused on this problem. I'm not sure if I should be using conservation of momentum, or what. Also do I have to compute the center of mass for the boat?

Thanks

 

[LowlyPion]

You don't think M_b is relevant to determining the momentum of the system?

 

[LowlyPion]

But to answer your confusion, yes, you are supposed to used conservation of momentum.

 

[haydn]

Ok, I'm still not really sure how to solve the problem. I don't even know where to begin really.

 

[LowlyPion]

When the ball is in the air, it has m1V1.

But if the boat was at rest when it was thrown and the friction is 0, then that means that the boat and people have opposite momentum doesn't it? But they of course have a different mass than the ball, so ...

 

[haydn]

I'm still confused how to set up the equations for parts A and B...

would it be, for part A:

(M_B+M₁+M₂)V_Boat = M_PV_P

 

[LowlyPion]

I'm still confused how to set up the equations for parts A and B...

would it be, for part A:

(M_B+M₁+M₂)V_Boat = M_PV_P

That looks right.

What happens then when it is caught?

 

[haydn]

M_PV_P = (M₁+M₂+M_B)V_{Boat, Final}

?

 

[LowlyPion]

M_PV_P = (M₁+M₂+M_B)V_{Boat, Final}

?

No. Because the momentums are in different directions aren't they and when it is caught what happens to the total momentum?

I should have pointed out before that the V of the boat and people was opposite to the Vp.

 

[haydn]

Ok, so in that first equation you said was right there should be a negative in front of V_Boat?

I don't know what happens when the backpack is caught... I thought all the momentum of the backpack would transfer to the boat+person system.

 

[LowlyPion]

Ok, so in that first equation you said was right there should be a negative in front of V_Boat?

I don't know what happens when the backpack is caught... I thought all the momentum of the backpack would transfer to the boat+person system.

It does.

But happily it must be the very same momentum that was imparted to the backpack when it was thrown.

Hence Momentum before throwing = momentum after being caught isn't it?

 

[haydn]

Ok great. I figured out the right answer now. Thanks for the help!