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116_PartUniversity Physics Solution

116_PartUniversity Physics Solution - 4-8 Chapter 4...

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4-8 Chapter 4 E VALUATE : The friction force on the box, exerted by the bed of the truck, is in the direction of the truck’s acceleration. This friction force can’t be large enough to give the box the same acceleration that the truck has and the truck acquires a greater speed than the box. Figure 4.30 4.31. I DENTIFY : Identify the forces on the chair. The floor exerts a normal force and a friction force. S ET U P : Let be upward and let y + x + be in the direction of the motion of the chair. E XECUTE : (a) The free-body diagram for the chair is given in Figure 4.31. (b) For the chair, so 0 y a = y y F ma = gives sin37 0 n mg F ° = and 142 N n = . E VALUATE : n is larger than the weight because F ! has a downward component. Figure 4.31 4.32. I DENTIFY : Identify the forces on the skier and apply m = F a ! ! . Constant speed means . 0 a = S ET U P : Use coordinates that are parallel and perpendicular to the slope. E XECUTE : (a) The free-body diagram for the skier is given in Figure 4.32. (b) x x F ma = with gives . 0 x a = 2 sin (65.0 kg)(9.80 m/s )sin 26.0 279 N T mg θ = = ° = E VALUATE : T is less than the weight of the skier. It is equal to the component of the weight that is parallel to the incline. Figure 4.32 4.33. I DENTIFY : m F = a ! ! must be satisfied for each object. Newton°s third law says that the force that the car exerts on the truck is equal in magnitude and opposite in direction to the force C on T F ! T on C F ! that the truck exerts on the car. S ET U P : The only horizontal force on the car is the force T on C F ! exerted by the truck. The car exerts a force on the truck. There is also a horizontal friction force C on T F ! f ! that the highway surface exerts on the truck. Assume the system is accelerating to the right in the free-body diagrams. E XECUTE : (a) The free-body diagram for the car is sketched in Figure 4.33a (b) The free-body diagram for the truck is sketched in Figure 4.33b.
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Newton°s Laws of Motion 4-9 (c) The friction force f ! accelerates the system forward. The tires of the truck push backwards on the highway surface as they rotate, so by Newton°s third law the roadway pushes forward on the tires. E VALUATE : and each equal the tension T in the rope. Both objects have the same acceleration T on C F C on T F a !
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