PROBLEM 15-52 (page 247, 13th edition) The 10 kg crate slides 3.5 m down the smooth free-rolling 40 kg ramp to B from rest at A. • Determine the speed of the ramp when the crate reaches B. • Determine the velocity of the crate when it reaches B. Express the velocity as a Cartesian vector in terms of speed and angle the velocity makes with the horizontal. • Determine the kinetic energies of the ramp and the crate when the crate reaches B. 3.5 m A 30° B O O D Figure: 15_P052 Copyright 02013 Pearson Education, publishing as Prentice Hall
15-52 (page 247, 13th edition) SUMMARY OF RESULTS (page 1) · Data mp = 40 kg ! = 30° · Velocities when the crate is at B m = 10kg hc = 3.5sin30°m Vp = ! 1.10 i m/s ! " V = 5.43, cos35.8 i !sin35.8 # o ! Jo% m/ ! " o ! 0 : $ V C/R # = 6.36 cos30 i ! sin30 J % m/ The crate slides down the ramp at angle ! = 35.8· to the horizontal. This is steeper than the plane angle ! = 30.0. because the ramp rolls to the left while the crate slides to the right and down the ramp. · Kinetic energies when the crate is at B (to hundredths of J) 1 m_v2 = = (40)(!1.1008)2 J =24.24 J 2 RR 2 1 2 2 m_v === (10)(5.4303)2 J =147.44 J The total kinetic energy is equal to the initial potential energy: mcghc =10(9.81)3.5sin30° J = 171.68J
15-52 (page 247, 13th edition) COMPLETION OF PROBLEM (page 2) · Data · Velocities mp = 40kg ‘R ! = 30° mc =10kg hc = 3.5sin30° m Vp = ! vpi ! Vc = Vc (cos' i "sin ! j) ! VC/R = VC/R ( cos' i "sin! j) • Unknowns VR VC VC/R ! We need four equations to determine the four unknowns.