Conservation of momentum prob

In summary, a wooden block is cut into two pieces with one piece having three times the mass of the other. A depression is made in both pieces and a firecracker is placed in it when the block is reassembled. The block is placed on a rough-surfaced table and the fuse is lit. When the firecracker explodes, the two blocks separate and slide apart. The ratio of distances traveled by each block is 1/3.
  • #1
pb23me
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Homework Statement


A wooden block is cut into two pieces, one with three times the mass of the other. A depression is made in both faces of the cut, so that a firecracker can be placed in it with the block reassembled. The reassembled block is set on a rough-surfaced table, and the fuse is lit. When the firecracker explodes, the two blocks separate and slide apart. What is the ration of distances each block travels?




Homework Equations


4mv=3mv-mv
4mv=0 so 3v=v


The Attempt at a Solution

I see that one velocity is one third of the other but I am not sure what answer to give as to how far each block travels?
 
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  • #2
You don't need to know how far, just the ratio of their distances.

Hint: If you run twice as fast as I do (and we start at the same time and go in opposite directions), what's the ratio of our distances from the starting point at any time? (Make up some numbers and see how it works.)
 
  • #3
ok it seems like it would just be 1/3
 
  • #4
That's it.
 
  • #5


I would approach this problem by first considering the conservation of momentum principle. This principle states that the total momentum of a system remains constant unless acted upon by an external force. In this case, the system consists of the two blocks and the firecracker.

Since the firecracker explodes, it exerts an external force on the system. However, the total momentum of the system before and after the explosion must remain the same. This means that the momentum of the two blocks after the explosion must be equal to the momentum of the original block before the explosion.

Using the equation for conservation of momentum, we can set the initial momentum (4mv) equal to the final momentum (3mv + mv). This gives us 4mv = 3mv + mv, which simplifies to 4v = 4v. This means that the velocity of the two blocks after the explosion is equal to the velocity of the original block before the explosion.

Now, we can use the equation for distance traveled (d = v*t) to determine the ratio of distances traveled by each block. Since the velocity is the same for both blocks, the ratio of distances traveled will be equal to the ratio of their masses. This means that the block with three times the mass will travel three times the distance of the other block.

In conclusion, the ratio of distances traveled by each block will be 3:1, with the larger block traveling three times the distance of the smaller block.
 

What is the conservation of momentum?

The conservation of momentum is a fundamental law of physics that states that the total momentum of a closed system remains constant over time, unless an external force acts on the system. In simpler terms, it means that momentum cannot be created or destroyed, only transferred from one object to another.

How is momentum calculated?

Momentum is calculated by multiplying an object's mass by its velocity. The equation for momentum is: p = m * v, where p is momentum, m is mass, and v is velocity. Momentum is typically measured in units of kilogram-meters per second (kg*m/s).

Can momentum be negative?

Yes, momentum can be negative. Momentum is a vector quantity, meaning it has both magnitude and direction. Negative momentum simply indicates that the object is moving in the opposite direction of its defined positive direction. For example, if an object is moving to the left, its momentum would be negative if the positive direction is to the right.

What is an elastic collision?

An elastic collision is a type of collision in which kinetic energy and momentum are conserved. In other words, the total kinetic energy and total momentum of the system before and after the collision are the same. This type of collision is often seen in billiards or other sports where objects collide without sticking together.

Can momentum be transferred between objects of different masses?

Yes, momentum can be transferred between objects of different masses. In fact, the change in momentum of an object is directly proportional to the force applied to it. This means that a smaller object can have the same change in momentum as a larger object if it experiences a greater force.

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