Centre of mass and translational motion

In summary, a 270 kg flatcar moving at 5.0 m/s along frictionless rails has a 90 kg worker walking from one end to the other at a speed of 3.0 m/s with respect to the car. Using the equation MVcm = m1v1 + m2v2, the speed of the center of mass is found to be 4.5 m/s. To find the distance traveled by the car, we can use the equation to determine the speed of the car while the man is walking. Using the given information, the speed of the man with respect to the ground can be expressed as V - 3 m/s.
  • #1
godwinscareer
27
0

Homework Statement



A 270 kg flatcar 20 m long is moving with a speed of 5.0 m/s along horizontal frictionless rails. A 90 kg worker starts walking from one end of the car to the other in the direction of motion, with speed 3.0 m/s with respect to the car.

Homework Equations



MVcm = m1v1 + m2v2

The Attempt at a Solution



I found the Vcm to be 4.5 m/s

I have no idea how to find the distance traveled by the car...can someone please help me
 
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  • #2
godwinscareer said:
I found the Vcm to be 4.5 m/s
How did you come up with that? (Hint: You are told that the initial speed of everything is 5.0 m/s.)
 
  • #3
I used the equation to find that...i don't know if its right or wrong..i don't know how to approach the problem
 
  • #4
The speed of the center of mass is given as 5.0 m/s. Since Vcm can't change, use that equation to figure out the speed of the car while the man is walking. Hint: If the speed of the car with respect to the ground is called +V, and the speed of the man with respect to the car is -3 m/s, what would be the speed of the man with respect to the ground in terms of V?
 

FAQ: Centre of mass and translational motion

1. What is the centre of mass?

The centre of mass is the point at which the entire mass of an object can be considered to be concentrated. It is the average position of all the mass of an object.

2. How is the centre of mass calculated?

The centre of mass is calculated by taking into account the mass and position of each individual particle that makes up an object. The centre of mass can be calculated using the formula:
xcm = (∑mixi) / (∑mi)
where xcm is the centre of mass, mi is the mass of each particle, and xi is the position of each particle relative to a chosen reference point.

3. What is translational motion?

Translational motion is the type of motion in which an object moves along a straight line without any rotation. It is a linear motion in which the object's position, velocity, and acceleration can all be described using one-dimensional equations.

4. How is translational motion related to the centre of mass?

The centre of mass plays an important role in translational motion. In a system with no external forces acting, the centre of mass will remain at a constant velocity and will move in a straight line. This is due to the fact that the centre of mass is the point at which all external forces can be considered to act on an object, resulting in a net force of zero and no acceleration.

5. Why is the concept of centre of mass important?

The concept of centre of mass is important because it allows us to simplify the analysis of the motion of complex objects. By considering the motion of an object as a whole, we can ignore the individual motions of each particle and focus on the motion of the centre of mass. This simplification is useful in many areas of science and engineering, such as in understanding the motion of planets, vehicles, and structures.

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