Conservation of Momentum and Relative Velocities

In summary, to find the lumberjack's speed relative to the shore, the equation of conservation of momentum is used. The lumberjack's initial velocity is multiplied by his mass and is equal to the negative product of the log's mass and the final velocity of the log and the lumberjack combined. After plugging in the given values, the final velocity of the log and the lumberjack combined is calculated to be -0.5826 m/s. This means that the lumberjack's speed relative to the shore is 2.7 m/s + (-0.5826 m/s) = 2.1 m/s. However, the answer provided is incorrect, so there may be an error in the previous steps.
  • #1
henry3369
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Homework Statement


An 82-kg lumberjack stands at one end of a 380-kg floating log, as shown in the figure (Figure 1) . Both the log and the lumberjack are at rest initially.

If the lumberjack now trots toward the other end of the log with a speed of 2.7 m/s relative to the log, what is the lumberjack's speed relative to the shore? Ignore friction between the log and the water.

Express your answer using two significant figures.

Homework Equations


Conservation of Momentum

The Attempt at a Solution


m1v1' + m2v2' = 0
m1v1' = -m2v2'
(82)(2.7) = (-380)(v2')
v2' = -0.5826

velocity in respect to shore = 2.7 + (-0.5826) = 2.1 m/s
For some reason this answer is incorrect. I also tried 2.7 + 0.5826 = 3.3 m/s, but that is wrong also. Is there something that I am doing incorrectly before this last step?
 
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  • #2
the 2.7 m/s is w.r.t the log, right ? But the 0.58 m/s can not be wrt the log. !
 

FAQ: Conservation of Momentum and Relative Velocities

What is conservation of momentum?

Conservation of momentum is a fundamental law of physics that states that the total momentum of a closed system remains constant over time, regardless of any external forces acting on it. This means that the total mass and velocity of the objects in the system will remain constant unless acted upon by an external force.

How is conservation of momentum related to relative velocities?

Conservation of momentum is related to relative velocities in that when two objects collide, the total momentum of the system before and after the collision must be equal. This means that the relative velocities of the objects before and after the collision will also be equal, but in opposite directions.

What are some real-world examples of conservation of momentum?

Some common examples of conservation of momentum include billiard balls colliding on a table, a rocket launching into space, and a car crash. In each of these situations, the total momentum of the system remains constant, even though individual objects may change direction or speed.

How does the mass and velocity of objects affect conservation of momentum?

In conservation of momentum, the total momentum of a system is equal to the total mass of the objects multiplied by their velocities. This means that if one object has a larger mass or velocity, it will have a greater impact on the total momentum of the system.

What is the importance of conservation of momentum in physics?

Conservation of momentum is a fundamental law in physics and is important because it helps explain and predict the behavior of objects in motion. It is also used in many engineering and technological applications, such as designing efficient car crashes or calculating the trajectory of a rocket.

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