Force (Newton's laws of motion)

In summary, when two people push in the same direction on an object of mass m, they cause an acceleration of magnitude a_1. When they push in opposite directions, the acceleration has a magnitude a_2. The magnitude of the force exerted by each person can be expressed as F_1 = 1/2 * m(a_1 + a_2) and F_2 = 1/2 * m(a_1 - a_2).
  • #1
pttest
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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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  • #2
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)
 
  • #3
thanks heaps
 

Related to Force (Newton's laws of motion)

1. What is Newton's first law of motion?

Newton's first law of motion, also known as the law of inertia, states that an object at rest will remain at rest and an object in motion will continue in motion with a constant velocity unless acted upon by an external force.

2. What is Newton's second law of motion?

Newton's second law of motion states that the force applied to an object is directly proportional to its mass and acceleration, and inversely proportional to its mass. This can be expressed as the equation F=ma, where F is force, m is mass, and a is acceleration.

3. How is Newton's third law of motion defined?

Newton's third law of motion states that for every action, there is an equal and opposite reaction. This means that when one object exerts a force on another object, the second object will also exert an equal and opposite force on the first object.

4. What is the difference between mass and weight in terms of Newton's laws of motion?

Mass is a measure of the amount of matter in an object, while weight is a measure of the force of gravity acting on an object. In terms of Newton's laws of motion, mass is used in the equation F=ma to calculate the force required to accelerate an object, while weight is the force that an object experiences due to gravity.

5. How does friction affect an object's motion according to Newton's laws of motion?

Friction is a force that opposes motion and is caused by the interaction between two surfaces. According to Newton's laws of motion, friction acts in the opposite direction of an object's motion, and can either slow down or stop the object's motion entirely.

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