Force (Newton's laws of motion)

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When two people push an object in the same direction, the total force exerted is equal to the mass multiplied by the acceleration (F_t = F_1 + F_2 = m * a_1). When pushing in opposite directions, the difference in their forces relates to the acceleration in the opposite direction (F_d = F_1 - F_2 = m * a_2). The equations derived show that the force exerted by the first person is F_1 = 1/2 * m(a_1 + a_2) and the force by the second person is F_2 = 1/2 * m(a_1 - a_2). This analysis effectively demonstrates how the forces relate to the object's mass and acceleration. Understanding these relationships is crucial for applying Newton's laws of motion.
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When two people push in the same direction on an object of mass {\rm m} they cause an acceleration of magnitude a_1. When the same people push in opposite directions, the acceleration of the object has a magnitude a_2. Determine the magnitude of the force exerted by each of the two people in terms of {\rm m}, a_1,and a_2. Express in terms of F1 & F2?
 
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Let the mass simply be m, since I have no clue what is {\rm m} is.

Let F_t be the total force pushed by those two people.
Then, F_t = F_1 + F_2 = m * a_1.
Let F_d be the difference of force between two people.
F_d = F_1 - F_2 = m * a_2.

Then, 2F_1 = m(a_1 + a_2)
F_1 = 1/2 * m(a_1 + a_2) (first person's force)
2F_2 = m(a_1 - a_2)
F_2 = 1/2 * m(a_1 - a_2) (second person's force)
 
thanks heaps
 

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