Physics 3200 TY2 quiz 3 handout #4 distributed September 13, 2017 You must show
ID: 1879213 • Letter: P
Question
Physics 3200 TY2 quiz 3 handout #4 distributed September 13, 2017 You must show all your work on this page. In the figure of the wedge below, position F lies at the midpoint of edge AC, while position G lies at the midpoint of edge BD. The sides of the wedge are two right triangles with side lengths of 72 mm, 96 mm, and 120 mm. Calculate the moment vector for the couple involving the two 40 newton forces. Your final answer should specify the x, y, and z components of the moment vector. 80 mm 60 mm/ 40 N 72 mm 60 mm 12.5 N 40 N 96 mm .t 12.5 NExplanation / Answer
for the couple involving two F = 40 N vectors
the moment arm is the perpendiculr distance between the two vectors
|M| = rF
r = 60*sin(phi)
tan(phi) = 80/60
phi = 53.13 deg
r = 48 mm
hence
|M| = 48*0.001*40 = 1.92 Nm
directino of this moment from the right hand rule is per pendicular to the inclined plane, and out of the plane
hecne the unit vector in this direction might be given by
n = (96/sqrt(96^2 + 72^2))j + (72/sqrt(96^2 + 72^2))k
n = 0.8j + 0.6k
hence
M = 1.536 j + 1.152 k Nm
where i , j and k are unit vectors along x y and z directions