What is the Force Exerted by the Ground on Object 1 in an Atwood Machine?

[antonisz]

1. A 77.00 Nt object (denoted as object 1) rests on the ground. A light cord is connected to this object which runs vertically upward over a light frictionless pulley and is attached to another object denoted as object 2.

a) Calculate the force that the ground exerts on object 1 if object 2 is 30 N.

b) Calculate the force that the ground exerts on object 1 if object 2 is 60 N.

c) Calculate the force that the ground exerts on object 1 if object 2 is 90 N.



http://imgur.com/cVEQW07 http://imgur.com/cVEQW07

g (m₁ - m₂) / (m₁) + m₂ = a_y I drew FBD's for both of the weights and solved for the acceleration for situation a. I then used the equation w - t = ma and solved for the tension value, I then subtracted the tension value from the original weight of object 1, and I got 33.88 N.

I feel like this is the wrong way of solving the problem because once you get to situation c, you would have a negative force which can't be possible.

 

[SammyS]

1. A 77.00 Nt object (denoted as object 1) rests on the ground. A light cord is connected to this object which runs vertically upward over a light frictionless pulley and is attached to another object denoted as object 2.

a) Calculate the force that the ground exerts on object 1 if object 2 is 30 N.

b) Calculate the force that the ground exerts on object 1 if object 2 is 60 N.

c) Calculate the force that the ground exerts on object 1 if object 2 is 90 N.



http://imgur.com/cVEQW07 http://imgur.com/cVEQW07

g (m₁ - m₂) / (m₁) + m₂ = a_y


I drew FBD's for both of the weights and solved for the acceleration for situation a. I then used the equation w - t = ma and solved for the tension value, I then subtracted the tension value from the original weight of object 1, and I got 33.88 N.

I feel like this is the wrong way of solving the problem because once you get to situation c, you would have a negative force which can't be possible.

That seems to be a correct result for part c. -- but ...

If the ground can't produce a negative (downward) force on m₁, then what do you suppose happens to the system?

 

[antonisz]

That seems to be a correct result for part c. -- but ...

If the ground can't produce a negative (downward) force on m₁, then what do you suppose happens to the system?

The system would change where object 1 would be "in the air" correct?

 

[SammyS]

The system would change where object 1 would be "in the air" correct?

Yes, so the ground will exert what force on m₁?

 

[antonisz]

Yes, so the ground will exert what force on m₁?

It would have to be 0 Newton's. If I'm correct about that, then I already assumed that, however I rethought my approach on part a and b.

I redid the FBD's for (a) and (b) and added the two equations for Newton's second law, and the tensions canceled each other out, leaving me with w₁ - w₂ = Fn. From there I calculated that in situation (a), the force that the ground exerts is 47 Newton's, and in situation (b) it would be 17 Newton's.

 

[SammyS]

It would have to be 0 Newton's. If I'm correct about that, then I already assumed that, however I rethought my approach on part a and b.

I redid the FBD's for (a) and (b) and added the two equations for Newton's second law, and the tensions canceled each other out, leaving me with w₁ - w₂ = Fn. From there I calculated that in situation (a), the force that the ground exerts is 47 Newton's, and in situation (b) it would be 17 Newton's.

That all looks good!

 

[antonisz]

That all looks good!

Thank you so much for the help!