# How Does Conservation of Momentum Apply in a Frictionless Sled Problem?

• PatsObi
In summary, a man of 70 kg stands on a sledge of mass 120 kg, initially 20 m away from the shore. He then walks 3 m towards the shore without friction. The man stops and the question is how far is he from the shore. Using the equation 70(Rm)+120(Rs)=0, where Rm and Rs are the distances from the man to the cm and the cm of the sledge to the cm respectively, we can find the center of mass of the system and use it to determine the final distance of the man from the shore after he stops.
PatsObi
I'm stuck on this problem.

A sledge of mass 120 kg is at rest on a horizontal icy surface. A man of mass 70 kg stands at one end of the sledge so the initially the distance from the man to the shore is 20 m. The man now walks 3 m relative to the sledge, towards the shore. The he stops. Assuming the moves w/out friction, how far from the shore is the man when he stops.

THis is pretty much all i know:

70(Rm)+120(Rs)=0

where Rm and Rs are the distances from the man to the cm and the cm of the sledge to the cm respectfully.

PatsObi said:
THis is pretty much all i know:

70(Rm)+120(Rs)=0

where Rm and Rs are the distances from the man to the cm and the cm of the sledge to the cm respectfully.

That is actually all you need, but with some understanding. Can you tell me what this eqn signifies? And how to find the CM of the system wrt the shore? After that, we can form the necessary eqns.

Also, the word you were looking for is "respectively", not respectfully.

Hello, I understand that you are stuck on the frictionless sled problem. It seems like you have already set up the equation using the distances from the man to the center of mass (cm) and the center of mass of the sledge to the cm. However, in order to solve this problem, we also need to consider the conservation of momentum and the conservation of energy.

First, we can start by setting up the conservation of momentum equation:

m1v1 + m2v2 = (m1 + m2)v'

Where m1 and v1 are the mass and velocity of the man, m2 and v2 are the mass and velocity of the sled, and v' is the final velocity of the combined system.

Since the problem states that the man initially stands at one end of the sledge, we can assume that the initial velocity of the sled is zero. This means that the equation becomes:

m1v1 = (m1 + m2)v'

Substituting in the values given in the problem, we get:

(70 kg)(3 m/s) = (70 kg + 120 kg)v'

Solving for v', we get:

v' = 1.82 m/s

Next, we can use the conservation of energy to find the distance from the shore where the man stops. We can set up the equation:

mgh = 1/2(m1 + m2)v'^2

Where m is the total mass (70 kg + 120 kg), g is the acceleration due to gravity (9.8 m/s^2), h is the distance from the shore where the man stops, and v' is the final velocity we calculated earlier.

Substituting in the values, we get:

(190 kg)(9.8 m/s^2)(h) = 1/2(190 kg)(1.82 m/s)^2

Solving for h, we get:

h = 0.17 m

Therefore, the man stops 0.17 m from the shore when he walks 3 m relative to the sled. I hope this helps you solve the problem. Remember to always consider the conservation of momentum and energy when solving physics problems involving motion. Good luck!

## 1. What is a frictionless sled problem?

A frictionless sled problem is a physics problem that involves a sled or object sliding on a surface with no friction. This means that there is no resistance or force acting against the motion of the sled, making it move without slowing down or stopping.

## 2. Why do scientists study frictionless sled problems?

Scientists study frictionless sled problems to understand the fundamentals of motion and to make mathematical models that can be applied to real-world situations. It also allows them to explore the effects of different variables, such as mass and velocity, on the motion of an object.

## 3. What are the key concepts involved in solving a frictionless sled problem?

The key concepts involved in solving a frictionless sled problem include Newton's laws of motion, conservation of energy, and the concept of inertia. It is also important to understand how forces, such as gravity, affect the motion of an object on a frictionless surface.

## 4. How do you solve a frictionless sled problem?

To solve a frictionless sled problem, you first need to identify the given variables, such as mass and velocity, and the unknown variable, such as acceleration. Then, you can use equations and principles of physics, such as Newton's second law, to calculate the unknown variable and solve the problem.

## 5. What are some real-world applications of frictionless sled problems?

Frictionless sled problems have many real-world applications, including studying the motion of objects in space, designing roller coasters, and understanding the movement of fluids. They also have practical applications in industries such as transportation, engineering, and sports.

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