# Solving Mechanics Problem with Mass & Momentum Conservation

• ColdFusion85
In summary: I understand the concept now.In summary, this is a problem involving the centre of mass and conservation of momentum on a frictionless surface. The man's movement changes the position of the centre of mass, but not its overall displacement. By using the relationship between the man and the sledge's mass and displacement, we can determine the final distance of the man from the shore after he stops.
ColdFusion85
I am stuck on a problem which goes as follows:

A sledge of mass 120kg stands at rest on the horizontal surface of an icy lake. A man of mass 70kg stands at one end of the sledge so that initially the distance from the man to the shore is 20m. The man now walks 3m relative to the sledge, towards the shore. Then he stops. Assuming that the sledge movies without friction on the ice, how far from the shore is the man when he stops?

Any guidance would be helpful. I don't need the answer, just a general way to go about finding distance in terms of mass and conservation of momentum.

ColdFusion85 said:
I am stuck on a problem which goes as follows:

A sledge of mass 120kg stands at rest on the horizontal surface of an icy lake. A man of mass 70kg stands at one end of the sledge so that initially the distance from the man to the shore is 20m. The man now walks 3m relative to the sledge, towards the shore. Then he stops. Assuming that the sledge movies without friction on the ice, how far from the shore is the man when he stops?

Any guidance would be helpful. I don't need the answer, just a general way to go about finding distance in terms of mass and conservation of momentum.
This is a centre of mass problem. The frictionless surface means that the centre of mass cannot move.

Assume that the sledge has uniform mass/unit length. Where is the centre of mass initially? Where is it in relation to the sledge after he moves? If that centre of mass is in the same position (relative to the ice sheet or the shore), where is the end of the sledge in relation to the shore?

AM

i'm still sort of stuck. the only thing i seem to know is that 70kg*v=120kg*u, and I am guessing that perhaps one has to use the relationship delta x = delta v \ delta t somehow.

ColdFusion85 said:
i'm still sort of stuck. the only thing i seem to know is that 70kg*v=120kg*u, and I am guessing that perhaps one has to use the relationship delta x = delta v \ delta t somehow.
Speed is irrelevant.

The centre of mass is a point (C) between the man (M) and the centre of the sledge (S) such that:

$70\vec{CM} + 120\vec{CS} = 0$ where CS is the displacement from C to S and CM is the displacement from C to M.

Since C does not change, this is still the relationship between CM and CS when the displacement between M and S decreases by 3. What does that tell you about how CS (and the position of the edge of the sledge) has changed? Since the man is 3 m. from the edge of the sledge, you know how far he is from the shore.

AM

## 1. What is the concept of mass conservation in solving mechanics problems?

The concept of mass conservation states that the total mass of a system remains constant, regardless of any internal or external forces acting on it. This means that the amount of mass entering a system must be equal to the amount of mass leaving the system.

## 2. How is momentum conservation used in solving mechanics problems?

Momentum conservation is a fundamental principle in mechanics that states that the total momentum of a system remains constant in the absence of external forces. This means that the initial momentum of a system must be equal to the final momentum after any interactions or collisions have occurred.

## 3. What are the equations used for solving mechanics problems involving mass and momentum conservation?

The equations used for solving mechanics problems with mass and momentum conservation are the conservation of mass equation, which states that mass in equals mass out, and the conservation of momentum equation, which states that initial momentum equals final momentum.

## 4. What are some common applications of solving mechanics problems with mass and momentum conservation?

Solving mechanics problems with mass and momentum conservation is commonly used in various fields of engineering, such as fluid dynamics, aerodynamics, and structural analysis. It is also used in physics to study the motion of objects and systems.

## 5. How can I improve my understanding and skills in solving mechanics problems with mass and momentum conservation?

To improve your understanding and skills in solving mechanics problems with mass and momentum conservation, it is important to have a strong foundation in mathematics and physics. Practice problems and seeking guidance from experts or tutors can also help improve your skills in applying these principles to solve problems.

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