Marble collisions, momentum, velocity

In summary, the conversation discussed a collision between two marbles, one with a mass of 5g and a speed of 20 cm/s, and the other with a mass of 10g and a speed of 10 cm/s. After the collision, the first marble continued with a speed of 8 cm/s in the same direction. The conversation then asked to calculate the momentum of each marble before and after the collision, as well as the speed of the second marble after the collision. Using the equation for momentum, the momentum of each marble before the collision was found to be 0.001 kg*m/s. However, in calculating the momentum after the collision, an error was made and the correct answer should have been 0
  • #1
KatieLynn
65
0

Homework Statement



Marble A, mass 5g moves at a speed of 20 cm/s. It collides with a second marble B, mass 10 g, moving at 10 cm/s in the same direction. After the collision, marble A continues with a speed of 8 cm/s in the same direction. A) Calculate the momentum of each marble before the collision. B) Calculate the momentum of each marble after the collision. C) What is the speed of marble B after the collision?

Homework Equations



F=m(Vf-Vi)/t


The Attempt at a Solution



I converted all the numbers first

Mass A= .005kg
Vi A = .2 m/s
Mass B= .1 m/s
Vi B = .2 m/s
V after = .8 m/s

A) Marble A:
(.005kg)(02m/s) = .001 kg*m/s

Marble B:
(.01kg)(.1m/s)=.001 kg*m/s

B) (.001+.001)=(.005kg+.01kg)V
v=1.33 m/s

What did I do wrong in B? I'm pretty sure A is right.
 
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  • #2
Just skimming over,

Total Momentum After = Total Momentum Before

P2' = P2

m2v2' = m2v2
(.01 Kg)(.08 m/s) = (.01 Kg)v2

algebra to isolate v2do you see what i did? Momentum after must equal momentum before, you know the momentum before the collision was m2v2, it has to equal momentum after, which is m2v2' your only unknown is v2' which you can solve using your data.. i did this usuing your definitions for the mass and velocities, i didn't check those.
 
Last edited:
  • #3


Your calculations for A are correct, but your calculation for B is incorrect. The formula for momentum is p=mv, where p is momentum, m is mass, and v is velocity. Therefore, the correct calculation for marble B after the collision would be:

p=mv
p=(0.01 kg)(0.1 m/s)
p=0.001 kg*m/s

This means that the momentum of marble B after the collision is the same as before the collision, since there is no external force acting on the marbles. This is known as the principle of conservation of momentum, which states that the total momentum of a system remains constant unless acted upon by an external force.

To find the speed of marble B after the collision, we can use the formula for momentum again:

p=mv
m=p/v
v=p/m

Substituting in the values from after the collision:

v=0.001 kg*m/s / 0.01 kg
v=0.1 m/s

Therefore, the speed of marble B after the collision is 0.1 m/s, or 10 cm/s. This is a decrease in speed from its initial velocity of 10 cm/s, which is expected since it collided with another marble and lost some of its momentum.

In summary, the momentum of each marble before the collision is 0.001 kg*m/s, and the momentum of each marble after the collision is 0.001 kg*m/s for marble A and 0.001 kg*m/s for marble B. The speed of marble B after the collision is 0.1 m/s.
 

1. What is momentum and how does it relate to marble collisions?

Momentum is the product of an object's mass and velocity. In the context of marble collisions, momentum is important because it determines the outcome of the collision. The momentum of each marble before and after the collision must be conserved.

2. How is velocity calculated in marble collisions?

Velocity is calculated by dividing the displacement of the marble by the time it takes to travel that distance. In marble collisions, the velocity of each marble can also be calculated by dividing its momentum by its mass.

3. How do different marbles with varying masses affect the outcome of a collision?

The mass of a marble affects its momentum, and therefore, the outcome of a collision. A heavier marble will have a higher momentum and can cause a smaller marble to change direction or stop completely upon collision. However, the conservation of momentum principle still applies, so the total momentum before and after the collision will be the same regardless of the masses of the marbles involved.

4. What are some factors that can affect the velocity of a marble during a collision?

The velocity of a marble during a collision can be affected by factors such as the angle of collision, the surface it is colliding on, and any external forces acting on the marble. Friction and air resistance can also play a role in altering the velocity of a marble during a collision.

5. How does energy play a role in marble collisions?

Energy is conserved during marble collisions, meaning that the total energy of the system before and after the collision will be the same. However, some energy may be converted into other forms, such as sound or heat, during the collision. The energy of the marbles can also affect their velocities and the outcome of the collision.

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