Solved: Force Problem x-axis [SOLVED] Force Problem

[Cursed]

[SOLVED] Force Problem

Homework Statement

Only two forces act on an object (mass = 3.00 kg), as in the drawing (below). Find the magnitude and direction (relative to the x-axis) of the acceleration of the object.

http://img148.imageshack.us/img148/6302/imgfbic2.png

Homework Equations

F=ma

The Attempt at a Solution

F=ma
40N=(3.00kg)(a)
13.33m/s/s=a

Correct answer: 30.9m/s/s, 27.2 degrees above the +x axis.

 

[princesspriya]

there are two forces acting on it so you would have to find the resultant force because you have to find the force net in order to use the F=ma equation. Finding the resultant by using vector addition method will give you the Force net and then you can plug in the mass to solve.

 

[Cursed]

there are two forces acting on it so you would have to find the resultant force because you have to find the force net in order to use the F=ma equation. Finding the resultant by using vector addition method will give you the Force net and then you can plug in the mass to solve.

I understand what you're saying, but I'm confused. I thought I knew how to calculate the resultant vector, but the way I'm calculating it leads me to the wrong answer.

Can you please show me how to do it? I would greatly appreciate it. ;)

 

[Doc Al]

Show how you calculated the resultant.

 

[Cursed]

Show how you calculated the resultant.

Okay.

I tried THREE ways:

1. I averaged the two vectors: .5(60N+40N) = 50N... Then I divided by 3 (since the weight is 3.00kg and F=ma). That equaled 16 and 2/3 m/s/s. Wrong.

2. I found the y component via Pythagorean theorem. It was √2000 = 44.7214N. Then I divided by 3 for the same reasons as #1. That equaled 14.97 m/s/s. Wrong.

3. I did R = r- r₀. (R being the resultant vector I am trying to find.). R = 40N. I divided it by 3 and got 13 and 2/3 m/s/s. Wrong.

 

[Doc Al]

Why in the world would you (attempt to) take the average?

In any case, do this: Find the x & y components of each vector. Add up the x components: that will be the x component of the resultant. Do the same with y components to find the y component of the resultant.

You can then find the magnitude of the resultant via the Pythagorean theorem.

 

[princesspriya]

you have to split the 60 N into two different vector quantities since it has a horizontal and vertical magnitude. the 40 N only has a horizontal quantity. then you would add the horizontal component of 60 and 40 to get the total force in the x direction.

 

[Cursed]

Why in the world would you (attempt to) take the average?

Haha, because none of the other ways I did it worked.

In any case, do this: Find the x & y components of each vector. Add up the x components: that will be the x component of the resultant. Do the same with y components to find the y component of the resultant.

You can then find the magnitude of the resultant via the Pythagorean theorem.

Thank you. I finally got the answer. :]

you have to split the 60 N into two different vector quantities since it has a horizontal and vertical magnitude. the 40 N only has a horizontal quantity. then you would add the horizontal component of 60 and 40 to get the total force in the x direction.

Thank you for your help too. :]