Multiple vector problem?

Question

The problem: A pack of six dogs is pulling on an old rag they found in an alley. Dog 1 is pulling with a force of 20N 20 degrees East of North, Dog 2 is pulling with a force 15N 35 degrees North of East, Dog 3 is pulling with a force of 10 N 25 degrees South of West, Dog 4 is pulling with a force of 25 N 18 degrees South of East, Dog 5 is pulling with a force of 5N due West and Dog 6 is pulling with a force of 25N 80 degrees East of South.

1) What is the force and direction the pack will move?

My answer: They will move 11.736 degrees North of East with a force of 54.601 N. I am sure that this is the right answer.

2) What is the magnitude and direction of the force that will cause the pack to stop moving?

This is the one I need help with. For the direction, I got 78.264 degrees. But what I don't know is how to get the magnitude. It would make sense for it to be 54.601N again, but it's apparently 74.3N and I don't know how this could be. If you know how that is, please help.

Answer 1

I will assume that you are right about 1 (maybe I will work it out later) but as for 2 the force to stop the pack must be equal and opposite to the resultant force. I am not sure what your angle is referring to since for all the others you say (East of North, etc) but for this one you don't. If you mean West of South then I would say it is correct and as for the magnitude I think you are right Suppose for a second that 74.3 was correct then the resultant force would not be 0 and the pack would be moving. Sometimes answer books and/or teachers and or professors can be wrong.

Oh well, I can't resist.

Dog1: 20[icos(70) + jsin(70)] ...... 20N 20 degrees East of North

Dog2: 15[icos(35) + jsin(35)] ...... 15N 35 degrees North of East

Dog3: 10[-icos(25) - jsin(25)] ...... 10N 25 degrees South of West

Dog4: 25[icos(18) - jsin(18)] ....... 25N 18 degrees South of East

Dog5:  5[-i] ............................... 5N due West

Dog6: 25[cos(10) - jsin(10)] ........ 25N 80 degrees East of South

for x-component:

20[cos(70)] +  15[cos(35)] - 10[cos(25)] + 18[cos(18)] - 5 + 25[cos(10)]

53.46123736

for y-component:

20[sin(70)] + 15[sin(35)] - 10[sin(25)] - 18[sin(18)] - 25[sin(10)]

11.10468692

Angle = 11.73 degrees North of East

Magnitude = 54.6 N

2 again.

Angle = 11.73 degrees South of West

Magnitude = 54.6 N

This will exactly balance the net force from the dogs and stop the rag from moving.

Don't see how it could be 74.3 unless the net force was aslo 74.3 which it isn't.