How High Will Each Ball Swing After Elastic Collision?

[Mdhiggenz]

Urgent! Pendulum problem elastic collision

Homework Statement

An elastic ball (A) with mass m is released from a horizontal position, connected via
a massless string to a rod. When the ball reaches the bottom, it collides with
another elastic ball (B) of twice the mass, aslo connected via a massless string to the rod.
How high can each ball swing, respectively? (The collision is total elastic.)
Assume the +x direction is to the right
a)What is the velocity of ball A after the collision? (5pt)
b)What is the velocity of ball B after the collision? (5pt)
c)How high will ball A swing relative to the bottom position? (5pt)
d)What is magnitude of the tension force (T) in the string connected to the ball A at the
moment right after the collision? (5pt)

A picture of the problem can be found at http://www2.fiu.edu/~leguo/Site/PHY2048_files/ExtraCredit2.pdf

Homework Equations

The Attempt at a Solution

M=Mtotal=3m
Va= initial velocity A

Vb= initial Velocity B

V1= final velocity A

V2= final velocity B

pi= initial momentum

pf= final momentum

ki = initial kinetic energy

kf= final kinetic energy



So what I first did was I wanted to find the initial velocity ( Va) before the collision.

To that I did: 1/2MVa^2=MgH
Va= √2gh

The collision is total elastic which means momentum and energy is conserved

Pi=pf

MaVa=Mav1+Mbv2

Im going to solve for v2:

MaVa-Mav1/Mb=v2

Plugging in known variables

m√2gh-mv1/2m=v2

m's cancel and you get

√2gh-v1/2=v2

Here is where I get confused my main problem lies with h. So I want to make that h cancel

since it is circular motion as the picture shows I try using uniform circular motion

g=Va^2/H

H= Va^2/g

I want to make sure if I am doing good so far. This is a problem that will be on my exam tomorrow so much help would be appreciated.

 

[churchmeng]

I'm attempting the same problem right now.

I took a different approach after final the initial velocity.

Since one object is stationary, I used the equations:

v_af = (m_a - m_b) / (m_a + m_b) * v_ai

v_bf = (2m_a) / (m_a + m_b) * v_ai

plugging in that gave me

(m-2m) / (m+2m) * √2gh
= -m / 3m * √2gh = -1/3 * √2gh

and

2m / m+2m * √2gh = 2m/3m *√2gh = 2/3 * √2gh

so the velocity of ball A after the collision is 1/3 the initial velocity in the opposite direction and the velocity of ball B is 2/3 the initial velocity of ball A in the +x direction

Can someone verify if this is correct?

 

[gneill]

I'm attempting the same problem right now.

I took a different approach after final the initial velocity.

Since one object is stationary, I used the equations:

v_af = (m_a - m_b) / (m_a + m_b) * v_ai

v_bf = (2m_a) / (m_a + m_b) * v_ai

plugging in that gave me

(m-2m) / (m+2m) * √2gh
= -m / 3m * √2gh = -1/3 * √2gh

and

2m / m+2m * √2gh = 2m/3m *√2gh = 2/3 * √2gh

so the velocity of ball A after the collision is 1/3 the initial velocity in the opposite direction and the velocity of ball B is 2/3 the initial velocity of ball A in the +x direction

Can someone verify if this is correct?

That looks okay