Find the Net Force and Acceleration Question

[iurod]

Homework Statement

The two forces F1 and F2 (shown in the figure) (i attached the figure hopefully I did it correctly) act on a 27.0 kg object on a frictionless tabletop. If F1=10.2N and F2= 16.0N, find the net force on the object and its acceleration for a and b

Homework Equations

F=ma

The Attempt at a Solution

If I'm approaching this correctly I believe its a simple vector addition problem?

for a I have:
x= -10.2
y= -16.0
this vector is = SQRT(-10.2² + -16.0²) = 18.97N

F=ma
19.97 = 27.0kg (a)
a= 0.70 m/s²

For b I have:
F2: x=0 y=16
F1: x=cos30 (10.2) = 8.8 y= sin30 (10.2) = -5.1

adding the x's together = 8.8
adding the y's together = 10.9

finding the vector= SQRT(8.8²+ 10.9²) = 14.0N
F=ma
14.0 = 27.0 kg (a)
a= 0.52 m/s²

Does this look correct?? Or did I even approach this correctly??

Thanks!

 

[kuruman]

It looks correct, but I think the problem really wants you to find the x and y components of the acceleration, not just its magnitude. Or, if you prefer to calculate magnitudes, then you must also specify a direction to define a vector unambiguously.

 

[iurod]

It looks correct, but I think the problem really wants you to find the x and y components of the acceleration, not just its magnitude. Or, if you prefer to calculate magnitudes, then you must also specify a direction to define a vector unambiguously.

Hi Kuruman,
Thanks for your help on this problem. So if I decide to find the magnitude of a vector I must also specify the direction? If I'm not mistaken is this done by taking the inverse tangent of opposite/adjacent?

for the first case tan^-1(-16/-10.2) = 57.5^o

and for the second case tan^-1(10.9/8.8) = 51^o


So for the part of the question that it asks for the net force is it safe to say that it is:

case 1 = 18.97N, 57.5^o

case 2 = 14.0N, 51^o

thanks.

 

[kuruman]

You still need to be a little careful and define the axis and direction with respect to which the angle is measured. The most common convention is "clockwise with respect to the positive x-axis". Personally and unless the problem states otherwise, I prefer to define vectors in terms of their components not magnitudes and angles.

 

[iurod]

You still need to be a little careful and define the axis and direction with respect to which the angle is measured. The most common convention is "clockwise with respect to the positive x-axis". Personally and unless the problem states otherwise, I prefer to define vectors in terms of their components not magnitudes and angles.

So if I'm following you correctly:

The components of the first situation is:
x= -10.2
y= -16.0
Theata = 51^o (when doing this I'm not entirely sure from what axis it is, I did tan^-1(-16/-10.2)

The components of the second situation:
x = 8.8
y = 10.9
theta = 51^o (again I don't know from which axis this is from, I did tan^-1(10.9/8.8)

Thanks for helping me with this!

 

[kuruman]

Part (a)
To find the angle you need a right triangle. It is the right triangle such that

tanθ = opposite/adjacent.

Draw yourself a right triangle such that one right side is 10.2 units to the left and the other right side is 16.0 unit down. To do this go to the tip of F₁ and draw a line segment of 16.0 units straight down. Connect the tip of that segment to the origin. There is your right triangle. Now answer the following questions

1. What is the angle that the hypotenuse makes with respect to the negative x-axis?
2. What is the angle that the hypotenuse makes with respect to the positive x-axis?
3. What does the 51^o that you found have to do with the above two angles?

If you can do this, then proceed the same way with part (b). In part (b) use the components that you found to draw another right triangle.

 

[iurod]

Part (a)
To find the angle you need a right triangle. It is the right triangle such that

tanθ = opposite/adjacent.

Draw yourself a right triangle such that one right side is 10.2 units to the left and the other right side is 16.0 unit down. To do this go to the tip of F₁ and draw a line segment of 16.0 units straight down. Connect the tip of that segment to the origin. There is your right triangle. Now answer the following questions

1. What is the angle that the hypotenuse makes with respect to the negative x-axis?
2. What is the angle that the hypotenuse makes with respect to the positive x-axis?
3. What does the 51^o that you found have to do with the above two angles?

If you can do this, then proceed the same way with part (b). In part (b) use the components that you found to draw another right triangle.

Ok, so I first drew a line with magnitude 10.2 going to the right (east), then I drew a line down (south) from the tip of east line. From there I drew a line from the tail of the east line to the head of the south line (tail to tip method). I have 10.2 as my x and 16.0 as my y. my hypotenuse has a magnitude of 18.97N pointing south east. my angle of the triangle is tan^-1= (16/10.2) = 57.5^o

1. The hypotenuse makes a 57.5^o with respect to the negative x axis.
2. the hypotenuse makes a 237.5^o with respect to the positive x axis.
3. The 51^o I initially got was probably a calculator error on my end, the angle of the line should be what is above in 1 and 2..

hopefully I'm now getting this, sorry to drag you through this with me, thanks again for your help!

If this is correct I know how to do it for the second case.

 

[kuruman]

1. The hypotenuse makes a 57.5^o with respect to the negative x axis.
2. the hypotenuse makes a 237.5^o with respect to the positive x axis.
3. The 51^o I initially got was probably a calculator error on my end, the angle of the line should be what is above in 1 and 2..

All of the above is correct. I think you understand what is going on. Proceed with part (b). By the way, in my earlier posting I was incorrect. The convention is "anti-clockwise with respect to the positive x-axis", which is what you calculated anyway. Sorry about the confusion.

 

[iurod]

All of the above is correct. I think you understand what is going on. Proceed with part (b). By the way, in my earlier posting I was incorrect. The convention is "anti-clockwise with respect to the positive x-axis", which is what you calculated anyway. Sorry about the confusion.

Awesome! I think this thread has helped me understand more than just the problem but on how to calculate the direction of a vector within a plane. Thank you so much for all your help, its greatly appreciated!