Calculating Displacement for a 2-D System

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To calculate the displacement of the center of mass for the olive-nut system, start by determining the initial center of mass using the respective masses and positions of the olive and Brazil nut. Next, apply Newton's second law to find the acceleration of each object based on the forces acting on them, and then use kinematic equations to calculate their positions after 3.1 seconds. Finally, compute the new center of mass position and determine the displacement by comparing it to the initial position. The key to solving this problem lies in correctly applying the equations of motion for both objects under the influence of the given forces.
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A big olive (m = 0.15 kg) lies at the origin of an xy coordinate system, and a big Brazil nut (M = 0.46 kg) lies at the point (0.72, 2.8) m. At t = 0, a force o = (1 + 1) N begins to act on the olive, and a force n = (-2 -4) N begins to act on the nut. What is the (a)x and (b)y displacement of the center of mass of the olive-nut system at t = 3.1 s, with respect to its position at t = 0?


The Attempt at a Solution



Im not too sure about going about solving this problem can anyone give me a head start?
 
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Break the problem into three parts:
1) Initial conditions
Find the center of mass of the olive-nut system.
Because this is a 2-d problem, apply the center of mass equation for each direction: x direction, and y direction.

2) Movement
Find out where the olive and nut moved to given the force on each and the time.

3) Final position
Find the final center of mass after they've moved.

Let me know if you need more details after you try it.
 
Anadyne said:
Break the problem into three parts:
1) Initial conditions
Find the center of mass of the olive-nut system.
Because this is a 2-d problem, apply the center of mass equation for each direction: x direction, and y direction.

2) Movement
Find out where the olive and nut moved to given the force on each and the time.

3) Final position
Find the final center of mass after they've moved.

Let me know if you need more details after you try it.

Okay, I found the xcom to be 0.108 and the ycom to be 1.288, but I don't know how to do part 2 because what equation do I use that involves force and time?
 
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