Learning Goal: A 1200-kg car is pushing an out-of-gear 2180 -kg truck that has a dead battery. When the driver steps on the accelerator, the drive wheels of the car push horizontally against the ground with a force of 4550 N. The rolling friction of the car can be neglected, but the heavier truck has a rolling friction of 770 N, including the "friction" of turning the truck's drivetrain. What is the magnitude of the force the car applies to the truck? PROBLEM-SOLVING STRATEGY 7.1 Interacting-objects problems MODEL: Identify which objects are part of the system and which are part of the environment. Make simplifying assumptions. VISUALIZE: Draw a pictorial representation. ■ Show important points in the motion with a sketch. You may want to give each object a separate coordinate system. Define symbols, list acceleration constraints, and identify what the problem is trying to find. ■ Draw an interaction diagram to identify the forces on each object and all action/reaction pairs. ■ Draw a separate free-body diagram for each object showing only the forces acting on that object, not forces exerted by the object. Connect the force vectors of action/reaction pairs with dashed lines. SOLVE: Use Newton's second and third laws. ■ Write the equations of Newton's second law for each object, using the force information from the free-body diagrams. Equate the magnitudes of action/reaction pairs. ■ Include the acceleration constraints, the friction model, and other quantitative information relevant to the problem. ■ Solve for the acceleration, and then use kinematics to find velocities and positions. REVIEW: Check that your result has the correct units and significant figures, is reasonable, and answers the question. Model The car and the truck are separate objects that form the system. Since only the straight-line motion of the car and truck is involved in this problem, model them as particles. The earth and the road surface are part of the environment. Visualize Assuming that the car pushes the truck to the right, which of the following free-body diagrams is the correct diagram for the situation described in this problem? In each case, the diagram on the left refers to the car, and that on the right to the truck. Dashed lines connect action/reaction pairs. The following notation is used: ƒ, n, and FG are, respectively, friction, normal force, and gravity; subscripts C and T stand for "acting on car" and "acting on truck"; F ConT is the force exerted on the truck by the car; and F Tonc is the force exerted on the car by the truck. Note that the force vectors are not drawn in scale. ▸ View Available Hint(s) Fron C y nc Car (FG)C y nc Car (FG)C FTC/ fc y nc (FG)C Car x Fr NT Fco C on T (FG)T Truck x Fr y NT FC on T (FG)T Truck x x fr y NT C on T +(Fa)T Truck Fron C y nc fc (FG)C Car x FT y nT FConT C on T +(FG)T Truck x fc y nc (FG)C Car x fr y NT FC on T +(FG)T Truck