engr 141 midterm

10 supports in 2-D and unknowns created

• cable/rope - one unknown which is tension force

• weightless link ( connects two things..?) - link imposes a force along its axis ( force in its direction)

• roller ( support with wheels) - one unknown , contact force

• rocker( support that rocks back and forth)- one unknown - contact force

• smooth contact ( smooth rod that contacts surface) - one unknown, contact force

• roller/pin confined in smooth slot ( wheel stuck in slot gap) - one unknown perp to slot ( think of direction it cant move in)

• member pin connected to collar on a smooth rod ( a rod that slids on another rod)- one unknow perp to smooth rod

• hinge/pin - 2 unknowns forces ( allows rotation tho)

• member pin fixed to collar on a smooth rod ( a rod that slids on another rod but this time the rod is fixed so edge of link cant swing)- 2 unknowns , 1 force perp to rod and one pure moment

fixed support ( no movement whatsoever allowed) - 3 unknowns in 2 -d abs every type of movement is restricited

best way to understand reaction forces from supports

• think of where movement or rotation is restricited - that creates a moment or force

two force member

-object with only 2 forces

in order for object to be in eq the forces must be equal mag op direction, along same line of action ( so no resultant moment)

three force member

all three forces must intersect at some point ( their Lines of action must intersect)

the could also all be parrelel but they have to be right mag ( balanced out)

cosin law

sin law

finding resultant angle of right triangle

if denom is neg add 180

for torque smallest force will always be force directly perpendicual to distance - since none gets wasted on parrelel compomnent

rectangular components

forces resolved along fx and fy

cartessian form

mag x direction vector ( unit lenght form)

dot product and cross product formula - angle between question!

coordinate direction angles

where alpha is angle between vector and pos x axis - can be taken for any direction ofc

moment of force about an axis

when solving for a moment in 2d

if ur not using the cross product u must use the RHR for direction silly girl!

counterclockiwse or out of the pg is positive

my rhr

fingers are r and palm is force

in wrenches when ur confused cause ur stuck with the mag of a moment

multiply that mag by the unit direction vector of the force! that gives u components then silly

couple moments generally not applied in journel bearings/pin/hinge if body is supported elsewhere

single thrust bearing prevents translation in direction of axis

fixed support number of unknowns ?

3 forces and 3 moments ( all 6)