Revisica
Sign in
ENGR5004 / Week 4
Dynamics L7 Worked example 2TutorialOld spec ENGR2162:115 min

ENGR216 Dynamics L7 worked example 2 (slides 11-13) official answers

Block A (mA=10m_A = 10 kg) rests on a horizontal surface with kinetic friction coefficient μk=0.2\mu_k = 0.2. A cord attached to A runs horizontally to a small pulley at the edge of the surface, down to a movable pulley from which cylinder B (mB=20m_B = 20 kg) hangs, and back up to a fixed hook on the ceiling (so B is supported by two cord segments). The cord is inextensible and the pulleys are frictionless and massless. At the instant considered, A is moving to the right (towards the edge) at 2 m/s and B is moving down.

Find the speed of A when it has moved 4 m to the right. Take g=9.81g = 9.81 m/s2^2.

Block A on a rough horizontal surface; the cord runs from A over a pulley at the edge, down around a movable pulley carrying cylinder B, and up to a ceiling hook. Axes: +X right, +Y down.
Block A on a rough horizontal surface; the cord runs from A over a pulley at the edge, down around a movable pulley carrying cylinder B, and up to a ceiling hook. Axes: +X right, +Y down.
Formulas you may need
  • Newton's second law: ∑F=ma\sum F = m a for each body (learn this)
  • Kinetic friction: F=μkNF = \mu_k N, opposing the sliding (learn this)
  • Dependent motion: write the cord length in position coordinates and differentiate (learn this)
  • Constant acceleration: v2=v02+2ac(s−s0)v^2 = v_0^2 + 2a_c(s - s_0) (learn this)