Determine the angle of incline

In summary: I omitted Fn and changed the equation to this:-Fgx + T = -m1a-4194.4sinθ + T = 0-4194.4sinθ = -4194.4-T = -2.94 – 196T = 198.94
  • #1
idlackage
11
0

Homework Statement



Determine the angle of incline on https://www.physicsforums.com/attachment.php?attachmentid=30517&stc=1&d=1291856979" frictionless air track.

Acceleration = 0.147 m/s2.

The answer is supposed to be 4.10°.

Homework Equations



Fnet = ma

The Attempt at a Solution



Mass 1 (https://www.physicsforums.com/attachment.php?attachmentid=30515&stc=1&d=1291856979"):

Perpendicular (y):

Fny = +Fn
Ty = 0
ay = 0
Fgy = -m1gcosθ
= (428)(-9.80)cosθ
= -4194.4cosθ
Fn + Fgy = 0
Fn = +4194.4cosθ

Parallel (x):

Fnx = 0
= -m1gxsinθ
= -4194.4sinθ
Fnet = m1a
Fn + Fgx + T = m1a

+4194.4cosθ – (-4194.4sinθ) + T
= (428)(0.147)
= 62.9

Mass 2 (https://www.physicsforums.com/attachment.php?attachmentid=30516&stc=1&d=1291856979"):

Fg2 = (20.0)(9.80)
= 196
Fg2 + T = m2a

196 + T = (20.0)(0.147)
= 2.94
T = 2.94 – 196
T = -490

Final calculations:

+4194.4cosθ – (-4194.4sinθ) + T = 62.9
(-) T = -490
----------------
+4194.4cosθ – (-4194.4sinθ) = 552

Not only do I not know how to solve that final equation, I'm also sure the answer will be wrong. I really don't get how to properly go about this question.
 

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  • #2
idlackage said:
Parallel (x):

Fnx = 0
= -m1gxsinθ
= -4194.4sinθ
Fnet = m1a
Fn + Fgx + T = m1a
Stop!. This equation is wrong. The normal force is along y (as you correctly point out) and does not belong in the x-equation. Furthermore, the tension is up the incline and the component of the weight is down the incline, so they must have opposite signs.
 
  • #3
kuruman said:
Stop!. This equation is wrong. The normal force is along y (as you correctly point out) and does not belong in the x-equation. Furthermore, the tension is up the incline and the component of the weight is down the incline, so they must have opposite signs.

Thank you! I omitted Fn and changed the equation to this:

Code:
-Fgx + T = -m1a
-4194.4sinθ + T
   = (428)(-0.147)
   = -62.9

So that the final calculations were:

Code:
    T = -62.9 + 4194.4sinθ
(-) T = -490
---------------------------
    0 = 427.1 + 4194.4sinθ
-427.1 = 4194.4sinθ
-427.1/sinθ = 4194.4
sinθ = -427.1/4194.4
   θ = sin-1(-427.1/4194.4)
   θ = 5.84°

Is this just a big percentage error, or am I still doing something wrong?
 
  • #4
The equation from the second FBD is also incorrect. The weight and the tension are in opposite directions. When you fix it, make sure that the direction of the acceleration is consistent between FBD1 and FBD2.
 
  • #5
I just realized I had no idea how I got 2.94 – 196 = -490 or other glaring errors. Is this correct?:

Code:
Fg2 - T = -m2a

196 - T = (20.0)(-0.147)
        = -2.94
-T = -2.94 – 196
T = 198.94

Final calculations:

    T = -62.9 + 4194.4sinθ
(-) T = 198.94
---------------------------
    0 = -260.94 + 4194.4sinθ
260.94 = 4194.4sinθ
260.94/sinθ = 4194.4
sinθ = 260.94/4194.4
    θ = sin-1(260.94/4194.4)
    θ = 3.57°
 
  • #6
That looks about right considering round offs. I got 3.55o.

*** On edit ***
Note that according to your drawing, arcsin(0.162/2.28) = 4.09o. If that's not close enough, you may have to explain the discrepancy.
 
  • #7
Awesome, thank you so much!
 

1. What is the angle of incline?

The angle of incline is the angle at which a surface is tilted or inclined from the horizontal plane.

2. How is the angle of incline determined?

The angle of incline can be determined by measuring the height and length of the inclined surface and using the formula tan θ = opposite/adjacent, where θ is the angle of incline.

3. What tools can be used to determine the angle of incline?

Various tools can be used to measure the angle of incline, such as a protractor, inclinometer, or a clinometer. In some cases, a smartphone app can also be used as a clinometer.

4. Why is it important to determine the angle of incline?

Determining the angle of incline is important in many fields, such as engineering, construction, and physics. It helps in understanding the stability of structures, calculating forces and movements, and designing efficient structures.

5. Can the angle of incline change?

Yes, the angle of incline can change if the surface is altered or if the object on the surface moves. It is important to regularly check and measure the angle of incline to ensure the safety and stability of structures.

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