Section 9.4: Collisions in 2 Dimensions

Elastic Collisions in 2Dimensions  v2i = 0 before Physical Principles: Same as in 1Dimension 1. VECTOR momentum conservation m1v1ix + m2v2ix = m1v1fx + m2v2fx m1v1iy + m2v2iy = m1v1fy + m2v2fy or m1v1i + 0 = m1v1f cosθ + m2v2fx cosφ 0 = m1v1fsinθ - m2v2fsinφ 2. Kinetic Energy Conservation (½)m1(v1i)2 + (½)m2(v2i)2 = (½)m1(v1f)2 + (½)m2(v2f)2 after

Ex. 9.4: 2 Car Collision at Intersection m1 = 1,500 kg, v1i = 25 m/s to the East  v1i = v1ix = 25 m/s, v1iy = 0 m2 = 2,500 kg, v2i = 20 m/s to the North  v2ix = 0, v2i = v2iy = 20 m/s Collision is perfectly inelastic So, cars stick together! θ = φ, v1f = v2f Find final velocities Momentum conservation: x: m1v1ix + m2v2ix = m1v1fx + m2v2fx or m1v1i + 0 = (m1 + m2)vf cosθ (1) y: m1v1iy + m2v2iy = m1v1fy + m2v2fy 0 + m2v2i = (m1+ m2)vfsinθ (2) (1) & (2) are 2 equations, 2 unknowns! Use algebra to solve! Results: vf = 15.6 m/s, θ = 53.1º (North of East)