How to Draw Force Diagrams for Suspended Objects and Equilibrium Situations

[santoki]

Homework Statement

1. An object with a mass of 300 kg is suspended between two cables which sag at an
   angle of 40ᴼ below horizontal, on either side. Draw a free-body diagram.
2. While driving in your car, you notice that the string holding the rosary to your
   rear-view mirror makes an angle of θ = 29ᴼ with respect to the vertical. The mass of the
   rosary is 0.06 kg. Consider the vertical forces on the rosary to be in equilibrium
   during this situation.

2. The attempt at a solution

 

[Andrew Mason]

Homework Statement

1. An object with a mass of 300 kg is suspended between two cables which sag at an
   angle of 40ᴼ below horizontal, on either side. Draw a free-body diagram.
2. While driving in your car, you notice that the string holding the rosary to your
   rear-view mirror makes an angle of θ = 29ᴼ with respect to the vertical. The mass of the
   rosary is 0.06 kg. Consider the vertical forces on the rosary to be in equilibrium
   during this situation.

2. The attempt at a solution

1. You have drawn the cable tensions at an angle of 50° below horizontal. Can you give us the magnitudes of all three forces and make the length of the vectors proportional to these magnitudes?

2. What is the question? Is this supposed to be a free-body diagram for the rosary? Does it show that the net vertical force is 0? (ie. that the rosary is in vertical equilibrium?). If there is a net horizontal force what is causing it? Why do you have 30° as the angle?

AM

 

[santoki]

1. You have drawn the cable tensions at an angle of 50° below horizontal. Can you give us the magnitudes of all three forces and make the length of the vectors proportional to these magnitudes?

2. What is the question? Is this supposed to be a free-body diagram for the rosary? Does it show that the net vertical force is 0? (ie. that the rosary is in vertical equilibrium?). If there is a net horizontal force what is causing it? Why do you have 30° as the angle?

AM

1. I will fix the lengths of the arrows according to their magnitude but does that mean the free-body diagram I have for #1 is correct?

2. I meant to write 30° in the question instead of 29°. I was just wondering if the free-body diagram I drew was correct. The diagram of the situation is below if it clears anything up:

 

[Andrew Mason]

1. I will fix the lengths of the arrows according to their magnitude but does that mean the free-body diagram I have for #1 is correct?

The angles of the tension vectors are incorrect.

2. I meant to write 30° in the question instead of 29°. I was just wondering if the free-body diagram I drew was correct. The diagram of the situation is below if it clears anything up:

If the diagram is correct then the car and the rosary are accelerating sideways (which could mean it is turning a corner or that it just got t-boned by a truck). Provided you make the length of the tension vector the correct length, it appears to be correct.

AM

 

[santoki]

The angles of the tension vectors are incorrect.

If the diagram is correct then the car and the rosary are accelerating sideways (which could mean it is turning a corner or that it just got t-boned by a truck). Provided you make the length of the tension vector the correct length, it appears to be correct.

AM

Would the #1 be correct if my tension vectors were pointing down since they are below the horizontal?

 

[Andrew Mason]

Would the #1 be correct if my tension vectors were pointing down since they are below the horizontal?

The reference to an angle "below the horizontal" refers to the angle the cable makes with the horizontal direction. That angle is the angle between the cable and the horizontal. You are showing 40° as the angle between the cable and the vertical direction.

AM

 

[santoki]

The reference to an angle "below the horizontal" refers to the angle the cable makes with the horizontal direction. That angle is the angle between the cable and the horizontal. You are showing 40° as the angle between the cable and the vertical direction.

AM

Oh I get it. 40° should be across the 90° since it is supposed to be the angle the horizontal direction and T₂ makes.