Question

Determine the moment of the force at AAA about point PPP. Use a vector analysis and express the result in Cartesian vector form. Determine the moment of the force at about point . Use a vector analysis and express the result in Cartesian vector form. MP=(−6i−3j−6k) kN−mMP=(−6i−3j−6k) kN−m MP=(24i+8j+9k) kN−mMP=(24i+8j+9k) kN−m MP=(−6i+6j−4k) kN−mMP=(−6i+6j−4k) kN−m MP=(24i−8j+9k) kN−mMP=(24i−8j+9k) kN−m

Answer 1

Answer:

τ = 0

Explanation:

At the moment it is defined

          τ = F x r

In tete case they give us the strength and position in Cartesian form, so it is easier to solve the determinant

      τ = $\left[\begin{array}{ccc}i&j&k\\F_{x}&F_{y}&F_{z}\\x&y&z\end{array}\right]$

Let's apply this expression to the exercise

a) P = (-6 i ^ -3j ^ -6 k ^) m

       F = (-6 i ^ -3j ^ -6k ^) 103 N

       τ =$\left[\begin{array}{ccc}i&j&k\\-6&-3&-6\\-6&-3&-6\end{array}\right]$  

       τ = i ^ (3 6 - 3 6) + j ^ (6 6 -6 6) + k ^ (6 3 - 3 6)

        τ = 0

b) P = 24i ^ + 8j ^ + 9k ^

     F = 24i + 8j + 9k

      τ = i ^ (72-72) + j ^ (216-216) + k ^ (24 8 - 8 24)

      τ = 0

c) P = -6i + 6j-4k

      F = -6i + 6j-4k

      τ = i ^ (24-24) + j ^ (- 24 + 24) + k ^ (-36 + 36)

      τ = 0

.d) P = 24i-8j + 9k

Let's change the sign of strength

     F = -24i + 8j-9k

   Tae = (I j k 24 -8 9 -24 8 -9)

   Tae = i ^ (72 -72) + j ^ (- 216 + 216) + k ^ (192-192)

    Tae = 0