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Elastic collision 
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#1
Feb2210, 10:34 PM

P: 25

1. The problem statement, all variables and given/known data
A ball is attached to one end of a wire, the other end being fastened to the ceiling. The wire is held horizontal, and the ball is released from rest. It swings downward and strikes a block initially at rest on a horizontal frictionless surface. Air resistance is negligible, and the collision is elastic. The masses of the ball and block are, respectively, 1.60 kg and 2.40 kg, and the length of the wire is 1.20 m. Find the velocity (magnitude and direction) of the ball (a) just before the collision, and (b) just after the collision. 2. Relevant equations .5m_{1}v^{2} = mgh m_{1}v_{1} + m_{2}v_{2} = m_{1}v_{f1} + m_{2}v_{f2} 3. The attempt at a solution So I've got part a ~ .5m_{1}v^{2} = mgh v^{2} = 2gh and I'm lost on part b: m_{1}v_{1} + m_{2}v_{2} = m_{1}v_{f1} + m_{2}v_{f2} since the final velocities of the ball and box are unknown how do I solve? 


#2
Feb2210, 10:48 PM

HW Helper
P: 4,433

After collision, total momentum and the KE is conserved.
Write down equations for these two conservation laws and solve for the final velocities. 


#3
Feb2210, 11:12 PM

P: 50

For b) since the ball collides with the block, initially at rest, you have to use the law of conservation of momentum and adding the block mass and the ball mass and using the speed in the above question as the initial velocity of only the ball: mava = v(mball +mblock), where mava = the speed and mass of the ball respectively from the above question. Therefore, Solve for v. Hope this helps:) 


#4
Feb2210, 11:29 PM

P: 25

Elastic collision
why would the final velocity be the same for both the ball and the block? 


#5
Feb2210, 11:53 PM

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P: 10,662

The velocities will not be the same after collision.
The collision is elastic, both the momentum and the energy is conserved during the collision. [tex]m_1v_{i1}+m_2v_{i2}=m_1v_{f1}+m_2v_{f2}[/tex] [tex]\frac{1}{2}m_1v_{i1}^2+\frac{1}{2}m_2v_{i2}^2=\frac{1}{2}m_1v_{f1}^2+\f rac{1}{2}m_2v_{f2}^2[/tex] Just before collision, the block is in rest, vi1=0, and the velocity of the ball is obtained from the equation vi2=sqrt(gL) where the length of wire is L=1.2 m. Calculate vi2 and plug in the values for the initial velocities in both equations. ehild 


#6
Feb2210, 11:59 PM

P: 50




#7
Feb2310, 12:24 AM

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The velocities will be the same if the collision is totally inelastic. ehild 


#8
Feb2310, 12:31 AM

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#9
Feb2310, 12:36 AM

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P: 10,662

ehild 


#10
Feb2310, 01:25 AM

P: 25




#11
Feb2310, 01:37 AM

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P: 10,662

No. Plug in the numbers and solve the system of equations.
ehild 


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