Elastic collision, one dimension

In summary: The negative sign just indicates a change in direction, but the magnitude of the momentum is still conserved. Your answers seem to be correct.
  • #1

Homework Statement



bloks b and c have m asses 2m and m respecti vely, and are at rest on a firctionless surface

black a also of mass m.. is heading at speed v toward block b as show... determine te final velocity of each block after alll subsequent collisions are over, assum all collision are elastic

aaaaaaa.jpg


Homework Equations

v_1f = (m_1-m_2/(m_1+m_2)) * v_1i + (2m_2/(m_1+m_2)) * v_2i

and

v_2f = (2m_1/(m_1+m_2)) * v_1i + (m_2-m_1/(m_1+m_2)) * v_2i

The Attempt at a Solution



i compared block A when it hits block B and then compared block C when block B hits it..

i got...

(m-2m / 2m+ m) * v

block a) - 1/3 v

found block b's v_i before it hits block c to be 2/3 v

(2m - m / 3m) *2/3v

block b) 2/9 v

(2*2m / 3m) *2/3v

block c) 8/9v
i feel confident these answers are right but just trying to see what others think
 
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  • #2
nightshade123 said:

Homework Statement



bloks b and c have m asses 2m and m respecti vely, and are at rest on a firctionless surface

black a also of mass m.. is heading at speed v toward block b as show... determine te final velocity of each block after alll subsequent collisions are over, assum all collision are elastic

aaaaaaa.jpg


Homework Equations




v_1f = (m_1-m_2/(m_1+m_2)) * v_1i + (2m_2/(m_1+m_2)) * v_2i

and

v_2f = (2m_1/(m_1+m_2)) * v_1i + (m_2-m_1/(m_1+m_2)) * v_2i

The Attempt at a Solution



i compared block A when it hits block B and then compared block C when block B hits it..

i got...

block a) - 1/3 v

found block b's v_i before it hits block c to be 1/3 v

Before a and b collide their total momentum is m_a * v

After the collision of a and b if v_a = -1/3 and v_b = 1/3

m_a*v_a + m_b*v_b = 1/3 m_a * v so momentum wasn't conserved
 
  • #3
mv + mv = mv + mv
ai -- bi -- af --bf
1 + 0 = 1/3 + 2/3

1 = 1 = momentum conservation...

negative for direction
 
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  • #5
nightshade123 said:
mv + mv = mv + mv
ai -- bi -- af --bf
1 + 0 = 1/3 + 2/3

1 = 1 = momentum conservation...

negative for direction

you had -1/3v for the speed of a. -1/3 + 2/3 isn't equal to 1.
If you substitute the right values in the formula for v2_f that you gave, you should get
the right value for the speed of b after the first collision.
 
  • #6
v_2f = (2m_1/(m_1+m_2)) * v_1i + (m_2-m_1/(m_1+m_2)) * v_2i

v_2f = (2*m / 3m) * v + 0

v_2f = 2/3v
 
  • #7
i think my answers now are correct, and the negitive on the 1/3 is for direction, doesn't mean that momentum is not being conserved
 
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  • #8
nightshade123 said:
i think my answers now are correct, and the negitive on the 1/3 is for direction, doesn't mean that momentum is not being conserved
True.
 

What is an elastic collision?

An elastic collision is a type of collision between two objects where both kinetic energy and momentum are conserved. This means that the total energy and momentum before and after the collision are the same.

What is the difference between an elastic and inelastic collision?

In an elastic collision, the objects bounce off each other with no loss of kinetic energy. In an inelastic collision, some kinetic energy is converted into other forms, such as heat or sound.

What is the equation for calculating the velocities of two objects after an elastic collision?

The equation is: v1f = ((m1 - m2) / (m1 + m2)) * v1i + ((2 * m2) / (m1 + m2)) * v2i and v2f = ((2 * m1) / (m1 + m2)) * v1i + ((m2 - m1) / (m1 + m2)) * v2i, where v1f and v2f are the final velocities of the two objects, m1 and m2 are their masses, and v1i and v2i are their initial velocities.

What is the coefficient of restitution?

The coefficient of restitution is a number that represents the elasticity of a collision. It is calculated by dividing the relative velocity of the objects after the collision by the relative velocity before the collision. A value of 1 indicates a perfectly elastic collision, while a value of 0 indicates a completely inelastic collision.

How does the mass of the objects affect the outcome of an elastic collision?

The mass of the objects affects the outcome of an elastic collision by determining the amount of kinetic energy each object has. The heavier the object, the more kinetic energy it has, and the greater the impact it will have on the other object during the collision. However, the final velocities of the objects will also depend on their initial velocities and the angle at which they collide.

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