1. Chap 5: 8 The Tow Truck

2. Model the Problem Forces on Car Cable Gravity Ramp Net Force

3. Horizontal and Vertical Components – On Car Will generally work – involves algebra Horiz Vert CableC cos 56° C sin 56° Ramp − normal force only θ = 65° Ramp−R cos 65° R sin 65° Grav 0 mg = −11,300 N Net 0 0

4. H & V equations Horizontal C cos 56° − R cos 65° = 0 Vertical C sin 56° + R sin 65° −11,300 N = 0 H:.559 C −.423 R = 0 V:.829 C +.906 R − 11,300 Newtons = 0 C = (.423 /.559 ) R =.756 R.829 (.756 R) +.906 R − 11,300 = 0.627 R +.906 R = 11,300 R = 11,300 / 1.533 = 7371 Newtons C =.756 R =.756 · 7371 = 5571 Newtons

5. Excel

6. Normal and Tangential on Car Can be easier Normal Tangential grav − mg cos 25° − mg sin 25° ramp R 0 cable C sin 31° C cos 31° net 0 0

7. Norm & Tang Equations Norm: − 11,300 cos 25° + R + C sin 31° = 0 Tang: − 11,300 sin 25° + C cos 31° = 0 − 4776 + C cos 31° = 0 C = 4776 / cos 31° = 4776 /.857 = 5571 R = 11,300 cos 25° − C sin 31° = 10,241 −.515 C = 10,241 − 2,869 = 7372