Engr Help

Principle of Work/Energy Plane Motion (example continued)

W_1-2= T₂ - T₁

Principle of Work/Energy

Work done by weight W_{1-2
weight} = ˗ mg d (3/5) = ˗ 30(6) = ˗ 180 ft lb

Work done by a spring W_{1-2 spring}= ½ k ( 0² ˗ d²) = ½ (10) ( 0² ˗ 10²) = ˗ 500 ft lb

Work done by P W_{1-2 P} = P d = 100(10) = 1000 ft lb

Next calculate the change in kinetic energy T₂ – T₁ = T₂ – 0 = T₂

T₂ = ½ m v_C² + ½ I^C_zz ω²

For a cylinder I^C_zz = ½ m r² = ½ (1)1² = ½ slug ft²

From kinematics (cylinder rolls without sliding) v_C = r ω Therefore ω = v_C / r

T₂ = ½ m v_C² + ½ ( ½ m) v_C² = (3/4) m v_C²

Finally equate the work done to the change in kinetic energy

˗ 180 ˗ 500 + 1000 = (3/4) (1) v_C² or v_C² = 320(4/3) v_C = √ (1280/3)

v_C = √ (1280/3) i ft/sec (result) Click here for another example.