Forces on Particle, Find Third Force?

[GingerBread27]

A lemon has three horizontal forces that act on it as it is on a frictionless table. Force F1 has a magnitude of 4.50 N and is at Angle1 = 26°. Force F2 has a magnitude of 7.00 N and is at Angle2= 26°. The lemon half has mass 0.0250 kg.
Picture is Attached.
What is the third force if the lemon half has the following velocities?


I did f1=4.5cos26i + 4.5sin26j
f2=7cos(-64)-7sin(-64)

THen I did f=(4.5cos26+7cos(-64))i+(-7sin(-64)+4.5sin36)j=7.11i+(-4.32j)

(a)At Zero velocity i got the I component to be -7.11 and the j component to be 4.32.
The j component is right but the i component is wrong and I don't know why.

(b)constant velocity v = (13.0 i - 14.0 j) m/s
(c)
varying velocity v = (13.0t i - 14.0t j) m/s, where t is time in seconds

What would I do to solve for B and C?

 

[vsage]

Your reference angles may be wrong. I would make all angles with respect to the polar axis (positive x axis) so that 26 degree angle would become 116. I'm not sure if I understand what part a is asking. What is the force if the velocity is 0i+0j? Is that it?

Just a little hint for part c (part b is essentially part a over again): take the derivative of their varying velocity equation to get the constant vector acceleration

 

[GingerBread27]

yes that is what they are asking. I don't understand why you would use 116 as the reference angle, either way I still get the wronganswer. ANd I don't understand what you mean by part b being part a again.

 

[vsage]

Sorry. I meant angle 1 is (180-26) degrees with respect to the polar axis and angle 2 is (-90+26) degrees with respect to the polar axis. use those and you should get a correct answer.

Part b is exactly part A because from what I can see the velocity is still constant meaning no net force is being applied to it.

 

[GingerBread27]

I don't see how using 154 as angle 1 would make the answers correct, since using angle1 as 26 degrees gave me the right j component.

 

[vsage]

Using it as an angle was correct because: sin(180-theta) = sin(theta) which you used in your j calculations correct? However, cos(180-theta) = -cos(theta) which messes you up on the i calculation. You basically found the force as if it was 26 degrees with respect to the polar axis. It is very important to choose the right angle.

 

[GingerBread27]

so the i component would be (4.5cos154)+7cos(-64)?

 

[vsage]

I believe so.

 

[GingerBread27]

It's wrong:( I don't understand. HOw can I get the J component and not the I!

 

[vsage]

hang on I'll work out the question. Give me a moment. Edit: is the homework online? "so the i component would be (4.5cos154)+7cos(-64)?"

Ok I worked it out. the i component IS what you mentioned (approximately -0.975i) but remember this value is -F3*cos(theta) because F1*cos(theta)+F2*cos(theta)+F3*cos(theta) MUST equal 0.

Now work out the j component. That would be -F3*sin(theta). See if you can't figure out the two unknowns given the two equations.

 

[GingerBread27]

online through webassign

 

[vsage]

(see above edit)

 

[GingerBread27]

i don't understand

 

[vsage]

What don't you understand specifically? You know since the object is stationary that it is in static equilibrium meaning that the sum of all the i components of the forces must equal zero as well as the sum of all the j components of the forces must equal zero (by Newton's second law). You found what the sum of forces F1 and F2 were but now you have to find F3 with components such that F1+F2+F3 = 0 in both the i and j directions. Manipulating the equation we find F1+F2 = -F3 or -(F1+F2) = F3.

 

[GingerBread27]

so if that's the case then wouldn't the i component of the third vector be just .976?

 

[vsage]

so if that's the case then wouldn't the i component of the third vector be just .976?

Yep it sure would.

 

[GingerBread27]

It was right, thank you so much. I'm sorry, but I just really don't understand this. Now for part b you said it was essentially the same as part a, so I thought you would just take f1+f2+f3=(13.0 i - 14.0 j) m/s but it's not working.

 

[vsage]

It was right, thank you so much. I'm sorry, but I just really don't understand this. Now for part b you said it was essentially the same as part a, so I thought you would just take f1+f2+f3=(13.0 i - 14.0 j) m/s but it's not working.

Well consider what you're doing. 13.0i - 14.0j is the velocity right? You can't just set forces equal to velocity. What does a constant 13.0i-14.0j velocity tell you about the net force?

 

[GingerBread27]

the net force is constant?

 

[vsage]

the net force is constant?

Well technically it is constant BUT consider what the velocity-time graph would look like. A straight line across would be it right? If acceleration is given by dv/dt, what is the acceleration?

 

[GingerBread27]

acceleration would be 0

 

[vsage]

Ok so how's b different from a then? :) C shouldn't be too far of a leap from A so I think you can get it with the hint I gave you.

 

[GingerBread27]

B is the same as A, since F=ma and a is zero. lol. Great. I'm wondering here why the mass was given because i haven't used it to calculate anything yet. Now for C the lemon is moving with respect to time, so there must be acceleration, right? So the net force wouldn't be equal to zero. Then what am I not seeing? lol

 

[vsage]

Right well if you have the velocity you know the acceleration since dv/dt = a

 

[GingerBread27]

I figured it out! :) THanks so much for your help :)