A force,
F = (2x + 5y) N,
is applied to an object at a point whose position vector with respect to the pivot point is
r = (2x + 4y + 5z) m.
Calculate the torque created by the force about that pivot point.
Torque is the F x r vector cross product.
Do your x, y and z represent unit vectors?
It is conventiuonal to use i, j and k for unut vectors along x, y and z orthogonal axes.
I am confused by your notation.
yes x,y, z is unit vectors.
To calculate the torque created by a force about a pivot point, we need to find the cross product of the position vector and the force vector.
The torque vector, τ, is given by the cross product of the position vector, r, and the force vector, F:
τ = r x F
First, let's calculate the cross product of the position vector and the force vector.
r x F = | i j k |
| 2x 4y 5z |
| 2 5 0 |
Expand this determinant using the formula for a 3x3 determinant:
= (4y * 0 - 5z * 5) i - (2x * 0 - 5z * 2) j + (2x * 5 - 4y * 2) k
Simplify each term:
= -25z i + 10z j + (10x - 8y) k
Therefore, the torque vector is given by -25z i + 10z j + (10x - 8y) k N.m.