Complicated Puck Problem (consevation of forces)

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In summary: Mass of green puckIn summary, the mass of the blue puck is 24.6% greater than the mass of the green puck. Before colliding, the pucks approach each other with equal and opposite momenta, and the green puck has an initial speed of 12.0 m/s at an angle of 33.5o. After the collision, half of the kinetic energy is lost and the blue puck has a mass of 1.246 times the mass of the green puck. Using conservation of momentum, the velocities of the pucks after the collision can be calculated.
  • #1
Chuck 86
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Homework Statement


The mass of the blue (dark) puck in the figure below is 24.6% greater than the mass of the green (light) one.

Before colliding, the pucks approach each other with equal and opposite momenta, and the green puck has an initial speed of 12.0 m/s. The angle q = 33.5o. Calculate the speed of the blue puck after the collision if half the kinetic energy is lost during the collision.

Homework Equations


EFx=0=M(Green)V(green)cos(x)-M(blue)V(blue)Cos(x)
EFy=0=M(green)V(green)sin(x)-M(blue)V(blue)Sin(x)

( (1/2M(blue)V(blue)^2+M(green)V(green)^2)/2)=(1/2)M(green)V(green)^2+(1/2)M(blue)V(blue)^2

M(green)V'(green)=M(blue)V'(blue)

M(green)= (M(blue))/(2.46)
M(blue)= (2.46)M(green)


The Attempt at a Solution


I think these equations are correct but i don't knbow how I am going to get the mass of them. That would help a lot
 

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  • #2
Chuck 86 said:

Homework Statement


The mass of the blue (dark) puck in the figure below is 24.6% greater than the mass of the green (light) one.

Before colliding, the pucks approach each other with equal and opposite momenta, and the green puck has an initial speed of 12.0 m/s. The angle q = 33.5o. Calculate the speed of the blue puck after the collision if half the kinetic energy is lost during the collision.

Homework Equations


EFx=0=M(Green)V(green)cos(x)-M(blue)V(blue)Cos(x)
EFy=0=M(green)V(green)sin(x)-M(blue)V(blue)Sin(x)

( (1/2M(blue)V(blue)^2+M(green)V(green)^2)/2)=(1/2)M(green)V(green)^2+(1/2)M(blue)V(blue)^2
The above says nothing at all. Perhaps you meant to write:

[tex]\frac{1}{2}M_{green}V_{green}^{'2} + \frac{1}{2}M_{blue}V_{blue}^{'2} = (\frac{1}{2}M_{blue}V_{blue}^2 + \frac{1}{2}M_{green}V_{green}^2)/2[/tex]

M(green)V'(green)=M(blue)V'(blue)
What is this?

Conservation of momentum means that the total momentum of the balls before collision is the same as the total momentum of the balls after:

[tex]M_{blue}\vec{V}_{blue} + M_{green}\vec{V}_{green} = M_{blue}\vec{V}'_{blue} + M_{green}\vec{V}'_{green}[/tex]

Now, using those two equations and the given information, try to find the velocities after collision.

AM
 
  • #3
.

I would like to first clarify that the problem is referring to the conservation of momentum, not conservation of forces. The equations provided are correct and can be used to solve for the speed of the blue puck after the collision.

To solve for the speed of the blue puck, we can use the given information that the green puck has an initial speed of 12.0 m/s and the angle between their initial momenta is 33.5 degrees. Using the equation EFx=0, we can set the initial momentum of the green puck (M(green)V(green)) equal to the final momentum of both pucks (M(green)V'(green) + M(blue)V'(blue)).

Next, we can use the equation EFy=0 to solve for the initial speed of the blue puck (V(blue)). This equation sets the initial momentum of the green puck (M(green)V(green)) equal to the final momentum of the green puck (M(green)V'(green)).

To solve for the mass of the pucks, we can use the given information that the mass of the blue puck is 24.6% greater than the mass of the green puck. This means that the mass of the blue puck is 2.46 times the mass of the green puck. Using this information, we can substitute for the mass of the blue puck (M(blue)) in the equations and solve for the speed of the blue puck after the collision.

After solving for the speed of the blue puck, we can use the equation ( (1/2M(blue)V(blue)^2+M(green)V(green)^2)/2)=(1/2)M(green)V(green)^2+(1/2)M(blue)V(blue)^2 to calculate the kinetic energy before and after the collision. We know that half of the kinetic energy is lost during the collision, so we can set the final kinetic energy equal to half of the initial kinetic energy and solve for V'(blue). This will give us the final speed of the blue puck after the collision.
 

What is the "Complicated Puck Problem (conservation of forces)"?

The Complicated Puck Problem is a physics problem that involves a puck sliding on a frictionless surface and colliding with different objects, such as walls or other pucks. The goal of the problem is to analyze the forces acting on the puck and determine its final velocity and direction after each collision.

What are the key principles involved in solving the Complicated Puck Problem?

The key principles involved in solving the Complicated Puck Problem are the conservation of forces and the law of momentum conservation. These principles state that the total force and momentum of a system remains constant unless acted upon by an external force.

What information is needed to solve the Complicated Puck Problem?

To solve the Complicated Puck Problem, you will need to know the initial mass, velocity, and direction of the puck, as well as the mass and velocity of any other objects involved in the collisions. Additionally, the angles and positions of the collisions must be known.

What are some common challenges when solving the Complicated Puck Problem?

Some common challenges when solving the Complicated Puck Problem include accurately measuring and calculating the forces and momentum involved, as well as taking into account any external factors, such as friction or air resistance. It is important to carefully track and account for all forces acting on the puck throughout the problem.

How can the Complicated Puck Problem be applied in real-world situations?

The Complicated Puck Problem has many real-world applications, such as in sports, engineering, and physics research. For example, it can be used to analyze the trajectory and impact of a hockey puck or a billiard ball, or to design and test the efficiency of collision avoidance systems in cars. It can also be used to study the conservation of forces and momentum in more complex systems, such as in astrophysics or molecular dynamics.

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