Help on Mechanics Question: Find BC Angle with Vertical

In summary, the problem involves finding the angle that the string BC makes with the vertical when a particle with mass 2kg is attached to strings AB and BC. The tension in BC is twice the tension in AB, and the particle is in equilibrium at 30 degrees with the vertical. By considering the horizontal components of the forces, we can set up two equations and solve for the angle using trigonometric functions. After correcting for some minor mistakes, the final answer is 14.5 degrees.
  • #1
Gughanath
118
0
I am revising for a test which is next week. I came across this question and I keep getting the wrong answer. Someone please help!

A particle has mass 2kg. It is attached at B to the end of two light inextensible strings AB and BC. When the particle is in equilibirum, AB makes an angle of 30 degrees with the vertical. The magnitude of the tension in BC is twice the magnitude of the tension in AB.

Find, in degress to one decimal place, the size of the angle that BC makes with the vertical.
:confused:
 
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  • #2
Do this in terms of "components". Let T be the tension is the string AB. Then the x component of force for the AB string is Tcos(30) and the y component is Tsin(30).
We don't know the angle the BC string makes with the vertical so call it θ. We do know that the tension in the BC string is "is twice the magnitude of the tension in AB." so it is 2T. The x component of force for the BC string is -2T sin(θ) (notice the negative- the two string pull in opposite directions horizontally) and the y component is 2Tcos(θ) (positive: both string pull upwards).
Since the object is not moving horizontally, the two x components must "offset":
T sin(30)- 2T sin(θ)= 0 or T sin(30)= 2T sin(θ).
Since the object is not moving vertically, the two y components, together, must equal the weight of the object: Tcos(30)+ 2Tcos(&theta)= 2g.
Can you solve those two equations for T and θ?
 
  • #3
I worked out the value of theta to be 90.4 degrees. I don't know where I am going wrong!
 
  • #4
I think you did a lilttle mistake. The X component of the AB string should be Tcos 60 and the y components is Tcos 30.
 
  • #5
oh sorry.my bad. Well I try again and get back to you!. Thanx
 
  • #6
The introductio of sin into the equation doesn't let me continue any further?
 
  • #7
Post your work, so we can help more!
 
  • #8
Hint: All you need consider are the horizontal components of the forces on the mass. Start there and show your work
 
  • #9
ok. I got two equations. 2Tcosθ + Tcos30 = 2g...1
Tcos60 = 2Tcos(90-θ) ...2
I have two simultanous equations. I rearrange equation 2 to make T the subject, and then sub T into equation 1.

Am I going the right way?
 
  • #10
The second equation is all you need.
 
  • #11
how? that doesn't make sense.
Tcos60 = 2Tcos (90-θ)
since cos 90 = 0, the equation simplifies to: Tcos60 = -2Tcos θ
cancel one T on each side>>>> cos60 = -tcosθ Now??
 
  • #12
FYI: In general, [itex]\cos (A - B) \ne \cos A - \cos B[/itex] !

Instead, cancel the T and get:
cos60 = 2cos (90-θ), and then
cos (90-θ) = (cos60)/2

Use your calculator.
 
  • #13
Doc Al said:
FYI: In general, [itex]\cos (A - B) \ne \cos A - \cos B[/itex] !

Instead, cancel the T and get:
cos60 = 2cos (90-θ), and then
cos (90-θ) = (cos60)/2

Use your calculator.
Oh no! Did I just make the mistake of the century? This is soo embarassing. OBVIOuSLY 2T/T is not T!...SHOOT ME...and yes, what you said is right. How could I forget these simple rules? all right..let me try again
 
  • #14
theta = 14.5 degrees!
 
  • #15
You got it.
 

FAQ: Help on Mechanics Question: Find BC Angle with Vertical

1) What is the definition of BC angle with vertical?

The BC angle with vertical refers to the angle formed between the line BC and the vertical line. It is also known as the angle of inclination or slope angle.

2) How do I find the BC angle with vertical?

To find the BC angle with vertical, you will need to use trigonometric functions such as sine, cosine, or tangent. The specific formula and steps will depend on the given information and problem context.

3) What is the importance of knowing the BC angle with vertical?

Knowing the BC angle with vertical is important in many practical applications, such as construction, engineering, and navigation. It helps determine the slope or inclination of a line or surface, which is crucial in designing and building structures or navigating through terrains.

4) Can the BC angle with vertical be negative?

Yes, the BC angle with vertical can be negative. This means that the line BC is sloping downwards from the vertical line. A positive angle indicates an upward slope.

5) Are there any alternate methods for finding the BC angle with vertical?

Yes, there are alternate methods for finding the BC angle with vertical, such as using a protractor or measuring device. However, these methods may not be as accurate or precise as using trigonometric functions and should only be used if necessary.

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