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Four movers pick up boxes. Each box has a different mass, and each mover applies a different amount of force to lift the box. Which box will have the greatest acceleration?

A. a 10 kg box lifted with 60 N of force
B. a 20 kg box lifted with 60 N of force
C. a 20 kg box lifted with 40 N of force
D. a 10 kg box lifted with 40 N of force

Respuesta :

Newton's second law allows us to find the greatest acceleration of the system is:

      1) In the case of vertical moment,  force cannot lift the box off the floor.

      2) In the case of horizontal movement, the system with the highest acceleration is:

           A. a 10 kg box lifted with 60 N of force

Newton's second law states that the net force on a body is proportional to its mass times the acceleration.  

         F = m a

where the bold indicates vectors, m is the mass and the acceleration of the body

In the attachment we have a scheme of the system for the two possible movements: vertical and horizontal.  

Vertical movements.

              F-W = ma

The weight of a body is the force with which the Earth attracts it.

          W = m g

           F - m g = ma

          a = F / m - g

Let's apply this formula to each case:

A. box of mass 10 kg and applied force F = 60 N

         a = 60/10 - 9.8

         a = -3.8 m / s

B. Mass of the box 20 kg and the force 60N

         

C. Mass 20 kg and force 40N

D. Mass 10 kg and F = 40 N

We can see that in all cases the force is not enough to lift the box off the floor.

If we assume that the motion is horizontal, Newton's second law.

             F = ma

             a = F / m

We apply to each case:

A) m = 10 F = 60 N

        a = 60/10

        a = 6 m / s²

B) m = 20 kg and F = 60n

         a = 60/20

         a = 3 m / s²

C) m = 20 kg and F = 40 N

         a = 40/20

         a = 2 m / s²

D) m = 10 kg and F = 40 N

          a = 40/10

         4 m / s²

In the case of a horizontal movement if we have acceleration, ordered from highest to lowest corresponds to the cases.

         A> D> B> C

In conclusion using Newton's second law we can find the greatest acceleration of the system is:

1) In the case of vertical moment, force cannot lift the box off the floor.

2) In the case of horizontal movement, the system with the highest acceleration is:

     A.   a 10 kg box lifted with 60 N of force.

Learn more here:  brainly.com/question/20332763

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