Tutorial 1 MECH 101 Liang Tengfei Office phone : Mobile : Office hour : 14:00-15:00 Fri 1

Outline Cartesian vector calculation(+ ×) 2D forces equilibrium problem Moment calculation Reduction of force system 2

Express a Force as a Cartesian Vector Magnitude + direction (daily life) a Cartesian Vector (statics analysis) 45۫ 60۫ F=200N 3

Exercise 1 + : resultant force F 1 =3 i-5 j+7 k, F 2 =-9 i+4 j-3 k F 1 +F 2 =? : Projection F 1 =3 i-5 j+7 k, e =0.6 j-0.8 k F 1 e=? ×: Moment F 1 =3 i-5 j+7 k, r =-9 i+4 j-3 k r×F 1 =? -6 i-1 j+4 k

2D forces equilibrium problem 5

Solution Step 1: Draw the Free-Body Diagram Isolating part of the cords system near point A, add the force. W=mg=(30kg) (10.0m/s 2 ) =300N, T BA,T EA are unknowns. 6

Step2 Select a coordinate system, and resolve the cord tensions into x and y components. Solution 7

Step3 Apply the Equilibrium Equation Step4 Solving these two equations, we find: Solution 8

Objects in Equilibrium An particle is in equilibrium ΣF = 0 2D  Rx=0,Ry=0  2 Equations, 2 Unknowns Why I don’t choose point B to analyze first? 9

practice 10

Review the Steps 1. Draw the Free-Body Diagram 2. Select a coordinate system and find the x and y components of every force 3. Apply the Equilibrium Equations 4. Solve the equations. 11

Exercise 2 dx dy N 12

Exercise 3 How many unkowns? 13 Find out the third equation:

Objects in Equilibrium An object is in equilibrium ΣF = 0 All the forces pass the same point. (particle) ΣF = 0 An object is in equilibrium If the forces don’t pass the same point, we need: ΣF = 0 & ΣM = 0 An object is in equilibrium 14

Moment The moment of a force about a point or an axis: a measure of the tendency of the force to rotate a body about that point or the axis. moment about a point ----A ball on the sea & The earth Moment about an axis ----The door & the handle 15

Moment about a point (general method) & (good for 3D) (don’t exchange r and F) o F d r If you can find the Moment arm d, it’s easier to use M=F*d. Especially in 2D problem, the direction of M is obvious. o F If F passes o, the moment of F about O is zero. 16

Example A 200-N force acts on the bracket shown in fig (a).Determine the moment of the force about point A 17

18

19

Which method is the best? 20

Moment about an axis What kind of force can roll the handle? 21 If the force is in the same plane with the axis, it doesn’t cause moment about the axis

Force system reduction 3 forces =>1 force to satisfy the mechanical effect is the same. 1. Resultant force should be the same 2. The resultant moment about an arbitrary point should be the same 22

Resultant force 23

Resultant moment 24

Think about: Force is an vector. Can this vector move arbitrarily? Can a couple move around? What’s the mechanical effect of a force? What’s the mechanical effect of a couple? 25

Reduce the distributed force Where is the centroid of the area of the load diagram? How to calculate the equivalent force? How to calculate the equivalent force? And where dose this concentrated force locate? 26

Example 27

Thank You! 28