Is this question dealing with law of conservation of momentum?

You are asked to use the given equation to determine the velocity of the canoe (m2) after the man (m1) starts moving.In summary, a man sitting in the back of a canoe that is at rest in a still pond begins to move forward at .50m/s relative to the shore. This leads to the question of what happens to the canoe. The given equation is used to determine the velocity of the canoe after the man starts moving.
  • #1
raek
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Homework Statement


A 75-kg man sits in the back of a 120-kg canoe that is at rest in a still pond. If the man beings to move forward in the canoe at .50m|s relative to the shore, what happens to the canoe?


Homework Equations


The equation they gave me is m1v1+m2v2 = m1v1'+m2v2'
I don't get it.


The Attempt at a Solution


I didn't really make an attempt. All I have on the paper is
(120 kg)(.50m|s) + ... I don't know what to put there. If it's even right!
 
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  • #2
You have 2 different parts. At rest and moving, aka before and after, aka primed and unprimed.
 
  • #3


Yes, this question does deal with the law of conservation of momentum. This law states that the total momentum of a closed system remains constant, meaning that the total momentum before an event must equal the total momentum after the event. In this case, the man and the canoe can be considered as a closed system, and the law of conservation of momentum can be used to determine what happens to the canoe when the man starts moving.

Using the given equation, we can set up the initial and final momenta for the man and the canoe. The initial momentum is 0 since both the man and the canoe are at rest. The final momentum for the man is (75 kg)(0.50 m/s) = 37.5 kg*m/s. The final momentum for the canoe can be calculated as (120 kg)(0 m/s) = 0 kg*m/s. Since the total momentum must remain constant, the final momentum for the man and the canoe combined must also equal 0 kg*m/s. Therefore, the final momentum for the canoe must be -37.5 kg*m/s in the opposite direction of the man's movement.

In other words, the canoe will move in the opposite direction of the man's movement with a velocity of -0.3125 m/s. This is an example of the law of conservation of momentum in action, as the total momentum of the system remains constant even though the man has started moving.
 

FAQ: Is this question dealing with law of conservation of momentum?

1. What is the law of conservation of momentum?

The law of conservation of momentum states that in a closed system, the total momentum of the system remains constant. This means that the total momentum before a collision or interaction is equal to the total momentum after the collision or interaction.

2. How is momentum defined in the law of conservation of momentum?

Momentum is defined as the product of an object's mass and its velocity. It is a vector quantity, meaning it has both magnitude and direction.

3. What is an example of the law of conservation of momentum in action?

One example is a billiard ball collision. When one billiard ball strikes another, the first ball loses momentum, but the second ball gains the same amount of momentum. This illustrates the conservation of momentum in action.

4. Does the law of conservation of momentum apply to all types of collisions?

Yes, the law of conservation of momentum applies to all types of collisions, including elastic and inelastic collisions. In elastic collisions, the objects bounce off each other and separate, while in inelastic collisions, the objects stick together after the collision.

5. How is the law of conservation of momentum related to Newton's third law of motion?

The law of conservation of momentum is closely related to Newton's third law of motion, which states that for every action, there is an equal and opposite reaction. This means that when two objects collide, the forces they exert on each other are equal and opposite, resulting in the conservation of momentum.

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