Calculate the moment about a point (5; 4; 3) ft. caused by the forces
P = 3^i - 2^j - 4^k lb. and Q = 5^i + 7^j - 2^k lb. acting at the points
(7; 2; -2) ft. and (-3; -2; 5) ft., respectively.
What I did was this;
vector r1= (7,2,2) - (5,4,3) = 2i-2j-5k
vector r2= (3,2,5) - (5,4,3) = -8i-6j+2k
Vector M1= (2i-2j-5k) X P = -7i-7j+2k
Magnitude= 7.55 ft-lbs
Vector M2= (-8i-6j+2k) X Q = -2i-6j+85k
Magnitude= 86.23 ft-lbs
Moment about the given point = (7.55) + (86.23) = 93.78 ft-lbs
I'm unsure if this is right
No one has answered this question yet.
To calculate the moment about a point caused by the forces, you need to follow these steps:
1. Find the position vectors (r) from the point to each force. In this case, you correctly found the position vectors:
r1 = (7, 2, -2) - (5, 4, 3) = 2i - 2j - 5k
r2 = (-3, -2, 5) - (5, 4, 3) = -8i - 6j + 2k
2. Take the cross product of each position vector with its respective force vector to obtain the moment vectors:
M1 = r1 x P = (2i - 2j - 5k) x (3i - 2j - 4k) = -7i - 7j + 2k
M2 = r2 x Q = (-8i - 6j + 2k) x (5i + 7j - 2k) = -2i - 6j + 85k
3. Calculate the magnitudes of each moment vector using the formula |M| = sqrt(Mx^2 + My^2 + Mz^2):
|M1| = sqrt((-7)^2 + (-7)^2 + 2^2) = 7.55 ft-lbs
|M2| = sqrt((-2)^2 + (-6)^2 + 85^2) = 86.23 ft-lbs
4. Finally, add the magnitudes of the two moment vectors to obtain the total moment about the given point:
Moment about the given point = |M1| + |M2| = 7.55 + 86.23 = 93.78 ft-lbs
Therefore, your calculation is correct. The moment about the point (5, 4, 3) ft caused by the forces P and Q is indeed 93.78 ft-lbs.