Finding direction of net force and direction of travel

[FL00D]

Homework Statement

A 0.35 kg particle moves in an xy plane according to x(t) = - 11 + 1 t - 6 t3 and y(t) = 19 + 3 t - 8 t2, with x and y in meters and t in seconds. At t = 0.7 s, what are (a) the magnitude and (b) the angle (within (-180°, 180°] interval relative to the positive direction of the x axis) of the net force on the particle, and (c) what is the angle of the particle's direction of travel?

Homework Equations

Fx=m(ax)
Fy=m(ay)

The Attempt at a Solution

I got the first part right by taking the second derivative of each plane and applying it to the equations.
(ax)= dvx/dt = -36t m/s^2
(ay) = dvy/dt = -16 m/s^2

and by applying the relevant equations
Fx= -8.82
Fy= -5.6

By using Pythagoras theorem I found that the net force to be
Fnet= 10.448
Which is right.

After drawing a picture
in part b my attempt to solve was
tan^-1(theta)= Fy/Fx

Which is tan^-1(theta) = -5.6/-8.82
theta = 32.41
which I got wrong

___________________________________________

Part C
My attempt was applying in the velocity functions of both planes which are

Vx= 1-18t^2
Vy= 3-16t

and finding that

Vx= -7.82
Vy= -8.2

After that
tan^-1(theta)= -8.2/-7.82
theta= 46.358

which I also got wrong.Thanks in advance.

 

[Student100]

For part B, what is the angle you found in reference to?

 

[gTurner]

Is this an online homework platform of some sort? If so, they may be sticklers for things like significant figures and so forth. To actually work through the problem, I'd have to take just a little time here.

 

[gTurner]

For part B, remember that the given interval is from -180 degrees to 180 degrees. Using the inverse trig functions will give you an angle, but they will always be between 0 and 90. It is up to you to determine from which axis the angle should be measured from and make the adjustment. Which quadrant does the total force lie in?

 

[Student100]

Is this an online homework platform of some sort? If so, they may be sticklers for things like significant figures and so forth. To actually work through the problem, I'd have to take just a little time here.

Significant figures don't matter right now. For raw computations with no analogue in experiment like this they don't ever matter except to teach people how to use them.

 

[FL00D]

For part B, remember that the given interval is from -180 degrees to 180 degrees. Using the inverse trig functions will give you an angle, but they will always be between 0 and 90. It is up to you to determine from which axis the angle should be measured from and make the adjustment. Which quadrant does the total force lie in?

Based on the drawing it should be in the 3rd quadrant.
I tried the negative angle and it was wrong.

 

[FL00D]

For part B, what is the angle you found in reference to?

In reference to the positive x-axis I suppose.

I am just confused now if I am supposed to use the negative angle or not because the net force is under the +x axis

 

[Student100]

Based on the drawing it should be in the 3rd quadrant.
I tried the negative angle and it was wrong.

What negative angle did you try?

In reference to the positive x axis.

The angle you found? No it isn't. It is in the third quadrant, like you stated, however.

 

[FL00D]

What negative angle did you try?
The angle you found? No it isn't. It is in the third quadrant, like you stated, however.

I think it was a wild try, makes no sense but I just added the negative sign.

What do you propose I should try

 

[Student100]

I think it was a wild try, makes no sense but I just added the negative sign.

What do you propose I should try

First you need to realize what the 32 whatever degree angle is in reference too. Then you need to draw an angle from the positive x-axis to the vector that results in an angle between [180, -180].

Draw a picture.

 

[FL00D]

First you need to realize what the 32 whatever degree angle is in reference too. Then you need to draw an angle from the positive x-axis to the vector that results in an angle between [180, -180].

Draw a picture.

I am sorry for the drawing's quality, it's my first time using this site.It makes sense that the angle relative to the +x axis is negative and it's less than 90.

but the angle I get is positive. What possible negative angle I could get ?

I tried using sin(theta) = Fy/F

sin^-1(theta) = -5.6/10.44
theta = -32.41

since sin and cosine give angles from (-180,180] shouldn't this be right ?

 

[Student100]

View attachment 89446

I am sorry for the drawing's quality, it's my first time using this site.It makes sense that the angle relative to the +x axis is negative and it's less than 90.

but the angle I get is positive. What possible negative angle I could get ?

I tried using sin(theta) = Fy/F

sin^-1(theta) = -5.6/10.44
theta = -32.41

since sin and cosine give angles from (-180,180] shouldn't this be right ?

No worries on drawing quality, but your picture is wrong. If you want to add $$F_y\hat{y}$$ and $$F_x\hat{x}$$ to produce $$\vec{F}$$ how would add them together graphically?

 

[FL00D]

No worries on drawing quality, but your picture is wrong. If you want to add $$F_y\hat{y}$$ and $$F_x\hat{x}$$ to produce $$\vec{F}$$ how would add them together graphically?

I realized my mistake, this one should be right ? So our angle is greater than 90 and is negative.

 

[Student100]

View attachment 89451

I realized my mistake, this one should be right ? So our angle is greater than 90 and is negative.

Correct, write a formula for that angle now, what is the 32 in reference to?

 

[FL00D]

Correct, write a formula for that angle now, what is the 32 in reference to?

It is in reference to the -x axis.

Theta = 180-32= 148 degrees in negative

 

[Student100]

It is in reference to the -y axis.

Theta = 180-32= 148 degrees in negative

That works, I would just say -180+32 = -148

Now retry part C!

 

[FL00D]

That works, I would just say -180+32 = -148

Now retry part C!

These are the velocity vectors and their sum

Shouldn't the angle be the same ? Or is it the same problem with the drawing ?

 

[Student100]

View attachment 89453

These are the velocity vectors and their sum

Shouldn't the angle be the same ? Or is it the same problem with the drawing ?

Same error with the drawling, redraw the resultant after adding the two component vectors.

 

[FL00D]

Same error with the drawling, redraw the resultant after adding the two component vectors.

Nice, thank you very much!

We had a whole chapter about vectors and we learned that we were supposed to do it the way I did it, why is it wrong for the velocity vector to be this way ?

 

[Student100]

Nice, thank you very much!

We had a whole chapter about vectors and we learned that we were supposed to do it the way I did it, why is it wrong for the velocity vector to be this way ?

Really, you guys learned to do it the wrong way then. Most likely you missed something or got confused when they were teaching it.

A vectors component can be represented by a vector itself by multiplying it with a base vector (what you were drawing.) Then to add them graphically you can place the head of one at the tail of the other, which produces 1/2 of a parallelogram. The resultant is from the beginning and terminal ends of the parallelogram.

So the way you're drawing it is the wrong way for any vector! What you're actually drawing is the displacement vector between two points.

 

[FL00D]

Really, you guys learned to do it the wrong way then. Most likely you missed something or got confused when they were teaching it.

A vectors component can be represented by a vector itself by multiplying it with a base vector (what you were drawing.) Then to add them graphically you can place the head of one at the tail of the other, which produces 1/2 of a parallelogram. The resultant is from the beginning and terminal ends of the parallelogram.

So the way you're drawing it is the wrong way for any vector! What you're actually drawing is the displacement vector between two points.

That's disappointing to know that I've learned something wrong.

Thank you very much. I really appreciate what you did here.

 

[Student100]

That's disappointing to know that I've learned something wrong.

Thank you very much. I really appreciate what you did here.

No problem, it's good to catch these misunderstands early! Glad I could help.