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Uniform Contact Forces What bodies interact with Block B? A 6 lb B 8 lb C 10 lb Table Block A? Block C? Yes No Yes No Gr Pi Gr Pi Table? Yes No Gr Pi Earth? Yes No Gr Pi Uniform Contact Forces Block A, block C and earth interact with block B. A 6 lb B 8 lb B C 10 lb Table Are the magnitudes of these forces known? (without using equilibrium) Block A on B? Yes No Gr Pi Block C on B? Yes No Gr Pi Earth on B? Yes No Gr Pi Uniform Contact Forces A 6 lb B B 8 lb C 10 lb Table The only force known without using equilibrium is due to gravity. Give symbols to the contact forces between blocks (equal and opposite): Force of B on A B A NAB NBC Force of A on B NAB NBC B C Uniform Contact Forces A 6 lb B 8 lb C 10 lb Table Free body diagram of B: NAB 8 lb NBC B Uniform Contact Forces A 6 lb B 8 lb C 10 lb Table Are these free body diagrams of A, B and C correct? NAB 6 lb NAB 8 lb 10 lb 8 lb NBC Yes No Ntable Gr Pi Uniform Contact Forces 6 lb 8 lb A B C 10 lb Table Correct free body diagrams are: 6 lb NAB ΣFy = NAB - 6 = 0 NAB = 6 lb NAB NBC 8 lb 10 lb NBC Ntable ΣFy = - NAB - 8 + NAB = 0 ΣFy = - NBC - 10 + Ntable = 0 NBC = 14 lb Ntable = 24 lb Uniform Contact Forces A 6 lb B 8 lb C 10 lb Table FBD of A 6 lb NAB FBD of B NAB 6 lb 8 lb 8 lb 10 lb NBC NBC FBD of C 10 lb Ntable Ntable FBD of A, B, and C as a unit Uniform Contact Forces What bodies interact with Blocks B and C as a pair? E D C C B B A Table Block A? Block D? Block E? Yes No Yes No Yes No Gr Pi Gr Pi Gr Pi Table? Yes No Gr Pi Earth? Yes No Gr Pi Uniform Contact Forces Is this the correct free body diagram of B and C as a unit? E (Blocks B and C are enlarged) D C WD B A C WC NBC B Yes No Gr Pi WB NAB Uniform Contact Forces How many errors there are in this FBD of B and C as a unit? E (Blocks B and C are enlarged) D WD C B WC C A NBC WB B NAB 1 Pi 2 Bl 3 Ye 4 Wh Uniform Contact Forces WD E C D NBC C B WC B WB A NAB Errors: WD is force of earth on D (not D on C) should not be in the diagram NDC is needed instead NBC which acts between bodies B and C should not be in the diagram Only forces exerted by other bodies on B and C (as a unit) are to be in the FBD Uniform Contact Forces FBD of B and C as a unit E NCD D C B A C B WC WB NAB Uniform Contact Forces Block is supported by a cord which exerts force on it through a washer : T cord on washer T cord on washer T block on washer T block on washer T washer on block T washer on block WB WB Force T exerted by the washer on block is equal the tension in the cord Uniform Contact Forces 1 Blocks rest on each other and are connected by cords. C B 2 A • cord exerts force on this block through a washer • cord passes through hole in this block and exerts no force on it Uniform Contact Forces 1 All blocks have equal weight W. Each pair of cords (e.g., pair 1 or pair 2) is located symmetrically about vertical centerline so both cords in a pair have the same tension. C B 2 A Determine tensions in cords 1 and 2, and forces between contacting blocks Uniform Contact Forces Is this the correct FBD of block B? 1 WC C B B WB T2 T1 T1 2 A Yes No Gr Pi T T2 2 Uniform Contact Forces Which of the forces in this FBD of block B are shown correctly? 1 WC C B WB T2 B T1 2 Yes WC No Gr Yes No Gr Pi T2 T1 Yes WB No Gr Yes T2 No Gr Pi A T1 Pi Pi Uniform Contact Forces 1 This is the correct FBD of block B NBC C B WB B T1 T1 2 WC A B WB T2 T1 T1 T2 Uniform Contact Forces Draw the FBD’s of each block A, B and C separately 1 C C B B 2 A A Uniform Contact Forces C WC T2 1 T2 NBC NBC C WB B B T1 2 A T2 T1 WA T2 A Block A: T2 = W/2 Block C: NBC = 2W Block B: T1 = 3W/2 Uniform Contact Forces 1 C B 2 A Draw the FBD of: blocks A, B, C and cord 2, as one unit. Uniform Contact Forces 1 FBD of blocks A, B and C and cord 2 as one unit WC C WB B T1 T1 2 A WA ΣFy = - 3W + 2T1 = 0 T1 = 3W/2