# ENGG 202 Lecture Notes - Lecture 1: Cross Product, Unit Vector, Contact Force

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Published on 26 Jan 2015

School

Department

Course

Professor

ENGG 202 Tutorial 5 February 5/6 2013

All problems are from old exams

30o

20o

P

A

Review – Equilibrium

1) The block has a weight of 100 N which acts at the

centre A. The surface is frictionless so the contact force is

normal to the inclined surface. What is the magnitude of

the force P required to hold the block in the equilibrium

position shown? ANS: 53.2 N

Solution Strategy: draw the FBD of the block.

There are 3 forces acting on the FBD, the weight (vertical), normal force perp to the surface, and

force P. Easiest would be to use a rotated set of axis (parallel and perp to slope)

Find the components of all the forces, write the eqns of equil and solve.

2) Determine the force acting along each strut (AB,

AC, and AD) necessary to hold the 200 N plant pot in

equilibrium. Points B and D lie in the x-z plane. Point

C lies in the y-z plane.

ANS: FAC = 250 N (away from A), FBA = 115 N

(toward A), FDA = 150 N (toward A)

Solution Strategy: draw the FBD of point A. it has 1

known (the weight) and 3 unknown forces (AD, AC,

AB) acting on it. The directions of the unknown forces

can be assumed as you wish (toward the point or away

from the point). Find the components of the forces

(magnitude is unknown so simply multiply the unit

vectors for each by a variable representing the force

magnitude.)

Sum the forces in the x, y, and z directions equal to zero and solve for the 3 unknown force

magnitudes. Negative answers tell you if your assumed directions are wrong (and therefore

opposite to the correct direction).

Moment about a point using scalars

3) Determine the direction θ (0 < θ < 180o) of the

40 N force F so that F produces (a) the maximum

moment about point A and (b) the minimum

moment about point A.

ANS: 63.4o, 153o

Solution Strategy: The maximum moment will occur when F is perpendicular to the line

connecting A to the point of application of F. The minimum moment will occur when the line of

action of F passes through point A.

F

2 m

4 m

A

θ