Revisica
Sign in
ENGR5004 / Week 4
Dynamics L7 Worked example 1TutorialOld spec ENGR2162:28 min

ENGR216 Dynamics L7 worked example 1 (slides 9-10) official answers

A uniform horizontal beam AB of length 2 m and mass mAB=100m_{AB} = 100 kg is built into a wall at A (fixed support). A crate of mass mC=15m_C = 15 kg is lifted by a motor-driven cable: the cable runs vertically up from the crate to a small pulley at the free end B of the beam, then horizontally (at the level of the beam axis) to a motor on a pier further to the right. The crate is accelerating upwards at 2 m/s2^2. Neglect the size and mass of the pulley; take g=9.81g = 9.81 m/s2^2.

Find the cable tension and the reactions at the fixed support A.

Cantilever AB (2 m) fixed to a wall at A; the cable from the crate rises vertically to a pulley at B and runs horizontally to a motor on a brick pier to the right; the crate accelerates up at 2 m/s^2.
Cantilever AB (2 m) fixed to a wall at A; the cable from the crate rises vertically to a pulley at B and runs horizontally to a motor on a brick pier to the right; the crate accelerates up at 2 m/s^2.
Formulas you may need
  • Newton's second law for the crate: ∑Fy=may\sum F_y = m a_y (learn this)
  • Static equilibrium of the beam: ∑Fx=0\sum F_x = 0, ∑Fy=0\sum F_y = 0, ∑MA=0\sum M_A = 0; a fixed support gives two forces and a moment (learn this)