Uniformly Accelerated Motion & Motion of Several Particles Section #11.6 Relative Motion – Dependent Bodies � Relative motion between ____________ particles �Changing x A in the pulley system ____________ ______________ �Need to determine ____________________ before proceeding with problem solution x B M A M B x A Pulleys - Procedure � Define positive directions � Add ____________________ at each cable connection Find cable length change: � If you need to “_________” cable to connect, _______ � If need to _________ cable to connect, _____________ � Total Δx=0, since cable does not get longer or shorter Pulleys - Procedure x A x B Δx A Δx B Pulleys - Procedure x A x B Δx A Δx B Given the velocity and acceleration of block A, find the velocity and acceleration of block B Example Problem #1 Example Problem #2 Given the velocity and acceleration of block B, find the velocity and acceleration of block A Exercise 2.5.20 (p. 87) Example Problem #3 Given the velocity and acceleration of block A, find the velocity and acceleration of block B Example Problem #4 � Block A has v A =10m/sec to the right at t=0 and a constant acceleration of 2.0 m/sec 2 to the left. � Find the distance traveled by the block B during the interval t=0 to t=8 sec. Example Problem #4a Draw: Given: Goal: (constant)2 10 2 0, s m a s m v A A += −= Assume: Equations: 2 0,0, 2 1 )( tatvyty BBBB ++= Example Problem #4b Solution: Pulley kinematics: Example Problem #4c 2 2 3 2 2 1 3 1 310)( t s m t s m mty B ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ −+ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ += t s m s m tv B ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ −+ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ = 2 3 2 3 1 3)( -2.0015.38 -1.3317.07 -0.6718.06 0.0018.35 0.6718.04 1.3317.03 2.0015.32 2.6713.01 3.3310.00 m/secmsec v B y B t jparker Microsoft PowerPoint - S3-Uniformly_Accelerated_Motion.ppt