EK Physics #280 and #281

[premed1001]

TIA!

http://gyazo.com/5b9a0f0e282c39c3a171babc930d024a

http://gyazo.com/83cce16448bb1163817a8c0ec0d7fe67

http://gyazo.com/c2b047616318efef875ccf354bab3332

especially in #281 how can the tension be equal to mg?

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[inasensegone]

EDIT: This is the long way to do it... skip down to my 2nd post for a shorter more intuitive method. Understand the math in this explanation though because it can still be applied to other problems if need be...

OK... I made a couple pictures in Latex for you. If you understand how to do problem 281, then you can figure out 280:

Here is the problem (This answer is for 281, but again, 280 is done similarly):

OK the object is not swinging back and forth, it's not accelerating left to right, it's perfectly still. It is in equilibrium. This means that the component of the tension acting in the X direction for T1 (denoted by the red line for T1) cancels out the x component for T2 (not shown). This component is given by basic trig relationships as T1Cosθ1 and T2Cosθ2 for T1 and T2 respectively. If you read EK, they go over this basic trig relationship ad nauseam. So now we have the following equation:

The components of the tension in the y direction also cancel. These are given by the T1, T2, and T3. T3 is simply the weight (mass* gravity). For problem 281, this is 1000 N. T3 acts downward, and partial components of T1 and T2 act upward. The component for T1 is represented by the blue line in the picture, and is given by T1Sinθ1 and T2Sinθ2 for T2 (not shown in the diagram). So now we get the following equation:

Now we have 2 equations and 2 unknowns. We can simply plug and chug. We simply need values for the angles as given by the following:

So now we plug these in and get the following for the x component:

(Here we can see that T1 = T2)

 

[inasensegone]

It seems I reached a picture limit:

This is for the y component:

We know from the previous x component equation that T1 = T2, therefore:

Therefore, T1 = 1000 N


***EDIT***
That is the long way to figure out that problem. Here is a quicker way:

We know that the tensions of the strings in problem 281 must be equal, because their angles are equal. Lets take a look at a 30-60-90 triangle:

This tells us that tension, which is represented here by x, is equal to 2 times the component in the x direction. If you orient this triangle to the picture in the problem, you will see that each tension will be equivalent to the weight of the object (1000 N) because at a 30 degree angle it only supplies a component equal to half this (500 N which is equal to the x/2 in the triangle). So while the tension is a thousand Newtons, the component that lifts up the mass is only 500. That's why we have 2 of them.

EDIT2: Here is a better representation of what I'm trying to explain:

Let me know if this answers your question.

Keywords for future searches: EK ExamKrackers 1001 Physics Question 281

 

[patrickmbyrne]

IDK what symbols I can use on here. So I'm going to use x1 for theta1 and x2 for theta2 instead of Θ.
Static equilibrium implies the sum of the forces is equal to zero. So Fnetx=0 and Fnety=0.
So write to equations for the forces. T1sin(x1)+T2sin(x2)=mg for vertical. Then T1cos(x1)=T2cos(x2). This implies T1=T2
T1sin(x1)+T1sin(x2)= mg then T1 (sin(x1)+sin(x2))=mg. T1=mg/(sin(x1)+sin(x2))=mg. That is mathematically how. Also if you think logically you can understand that a smaller angle is proportional to a larger vertical tension(smaller horizontal) in the rope.

 

[premed1001]

Thank You!

 

[premed1001]

http://gyazo.com/47d255b4294fd90c979ceb990752560e

http://gyazo.com/8934abee9b2113e7aeb38ee731e98115

if anyone can explain the intuition here

thanks!!

 

[premed1001]

http://gyazo.com/47d255b4294fd90c979ceb990752560e

http://gyazo.com/8934abee9b2113e7aeb38ee731e98115

if anyone can explain the intuition here

thanks!!

nevermind, think i got it