Measuring Vectors: Force Exerted on Tripod Legs

In summary, The relationship between the position and force vectors can be established by assuming that the legs only take forces in the longitudinal direction, resulting in a proportional relationship between the force vector and the difference vector between the camera position and the leg position.
  • #1
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vector.jpg

Homework Statement


This is an example problem in my calculus textbook. I don't get how they relate the position vector to the force vector. I have taken a calculus based physics course and I don't remember establishing such relationship between the position and the force vectors.

Note: I have attached a picture of the situation.
[/B]
A television camera weighing 120 pounds is supported by a tripod, as shown in Figure 11.23. Represent the force exerted on each leg of the tripod as a vector.

Homework Equations


u=cv
v + u= v1 + u1, v2 + u2, v3 + u3
cv=cv1, cv2, cv3

3. The Attempt at a Solution
Let the vectors and represent the forces exerted on the three legs. From Figure 11.23, you can determine the directions of and to be as follows:[/B]

PQ1= <0,-1,-4>
PQ2= <√3/2, 1/2,-4>
PQ3= <-√3/2, 1/2,-4>


Because each leg has the same length, and the total force is distributed equally among the three legs, you know that the magnitude of F1=F2=F3. So, there exists a constant such that

F1= c<0,-1,-4>=F2= c<√3/2, 1/2,-4>=F3= c<-√3/2, 1/2,-4>
Let the total force exerted by the object be given by F= <0,0,-120> Then, using the fact that

F= F1 + F2 + F3


you can conclude that F1, F2, and F3 all have a vertical component of -40. This implies that c(-4)= -40 and c is equal to 10.
Therefore, the forces exerted on the legs can be represented by

F1= <0,- 10, -40>
F2= <5√3, 5, -40>
F3= <-5√3, 5, -40>
 
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  • #2
The assumption is that the legs only take up forces in the longitudinal direction and therefore must take a force in the direction they are pointing.
 
  • #3
Orodruin said:
The assumption is that the legs only take up forces in the longitudinal direction and therefore must take a force in the direction they are pointing.

I'm sorry, but I am still not very clear on this.
 
  • #4
It is an assumption (which will tend to be well founded). If the legs only take forces parallel to themselves, then the force in a leg must be proportional to any vector which is parallel to the leg. In particular, the difference vector between the camera position and where a leg stands is parallel to the leg.
 

1. What is a vector?

A vector is a mathematical representation of a physical quantity that has both magnitude and direction.

2. How do you measure vectors?

Vectors can be measured by using a variety of tools such as rulers, protractors, and force sensors. The magnitude of a vector can be measured in units such as meters, kilograms, or newtons, while the direction can be measured in degrees or radians.

3. What is force exerted on tripod legs?

Force exerted on tripod legs is the amount of force applied to the legs of a tripod, which is used to stabilize and support a camera or other equipment. This force is typically measured in newtons or pounds.

4. Why is it important to measure the force exerted on tripod legs?

Measuring the force exerted on tripod legs is important because it helps ensure that the tripod is able to support the weight of the equipment placed on it. This can prevent damage to the equipment and ensure stable and accurate images or measurements.

5. What factors can affect the force exerted on tripod legs?

The force exerted on tripod legs can be affected by various factors such as the weight and distribution of the equipment placed on the tripod, the angle and position of the tripod legs, and external forces such as wind or movement of the ground.

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