# Collision/conservation of linear momentum

## Homework Statement

A simple pendulum consists of a 1.50 kg mass connected to a cord without any mass or friction. Initially the pendulum is vertically positioned when a 2.00 kg mass collides with it, causing the pendulum to displace vertically upward 1.25 m. After the collision, the 2.00 kg mass travels along the frictionless horizontal surface, until it meets a 30 degree incline with a coefficient of kinetic friction of .400. If the mass travels a maximum distance of 1.125 m up the incline, determine the initial velocity that the 2.00 kg mass strikes the pendulum with.

## Homework Equations

I used:

Po=Pf Original Momentum = to Final Momentum
M1V1o+M2V2o=M1V1f+M2V2f Conservation of Linear Momentum
P=MV
Ei=Ui+Ki
Ef=Uf+Kf
U=MGh
Ki=1/2MVi^2
Kf=1/2MVf^2
(Uf-Ui)+(Kf-Ki)=-fd
MGYf+MGYo+1/2MVf^2-1/2MVo^2=The coefficient of friction times Nd
sin(theta)=Y/d

Sorry for the poor organization, All lower case letters are meant to be subscript except for the "h" in "U=MGh" and the "d" at the end of the last two equations.

## The Attempt at a Solution

I've been working on this for a few days, I think I may have come up with something. I believe the final velocity of the pendulum when it reaches 1.25m height is 4.95 m/s. Also, I'm having difficulty dealing with the 30 degree incline and how that affects the velocity of the 2.00kg mass. I got a velocity of 2.57 m/s when the mass reaches the base of the incline but am not sure where to go from there.

Edit: I think I may have gotten an answer. I used the conservation of linear momentum equation with the velocity of the pendulum and the velocity of the mass at the base of the incline. I got the initial velocity of the 2.00kg mass to be 6.28 m/s. If anyone can confirm this or tell me where I went wrong I would really appreciate it.

## Answers and Replies

rl.bhat
Homework Helper
Your initial velocity ( not the final ) is correct. When the 2 kg mass in moving up the inclined plane, what is the total force acting on it so that it stops after moving certain distance?

Your initial velocity ( not the final ) is correct. When the 2 kg mass in moving up the inclined plane, what is the total force acting on it so that it stops after moving certain distance?

By my initial velocity are you saying that the initial velocity that the 2.00kg mass strikes the pendulum with is correct? Or are you saying that the velocity when the mass approaches the ramp is correct? Is the final velocity of the pendulum at the top of its swing wrong? Sorry, just want to clarify exactly what you're saying.

I'm actually checking this forum for my fiancee while she is away from the house, so I'm not exactly sure how to do any of this until she gets back. She would like to know what information she would need to use to find the force acting on the 2kg mass on the inclined plane. In the problem you are also told g=9.80 m/s^2

rl.bhat
Homework Helper
By my initial velocity are you saying that the initial velocity that the 2.00kg mass strikes the pendulum with is correct? Or are you saying that the velocity when the mass approaches the ramp is correct? Is the final velocity of the pendulum at the top of its swing wrong? Sorry, just want to clarify exactly what you're saying.
It is non of these. It is the initial velocity of 1.5 kg.

I'm still not really sure what you mean. You said the initial velocity of 1.5kg. The initial velocity of the 1.5kg mass is 0. It is still on a pendulum and is struck by the 2kg mass. I need to find the initial velocity that the 2kg mass strikes the pendulum with.

rl.bhat
Homework Helper
I'm still not really sure what you mean. You said the initial velocity of 1.5kg. The initial velocity of the 1.5kg mass is 0. It is still on a pendulum and is struck by the 2kg mass. I need to find the initial velocity that the 2kg mass strikes the pendulum with.
After impact of 2 kg mass, what is the initial velocity of 1.5 kg of mass? That is what you have found. Now you have to find out what is the velocity of 2 kg mass when it starts climbing the inclined plane.

Ok, we've been working on this this whole time. We found the velocity of the 2kg weight after collision to be 4.32 m/s resulting in a final answer of the initial velocity of the 2kg weight being 8.0325 m/s. Is any or all of this right?

I was wondering if anyone ever figured this one out completely? I think that if you get the initial velocity of the 2.00kg mass at the base of the incline then that can be used as the final velocity after it strikes the 1.50 mass, and so can be used in this equation
MVinitial + mVinitial = MVfinal + mVfinal
Is this correct thinking?