Chapter 4 Quick Check Problems

Quick Check 4.1 The net force on an object points to the left. Two of three forces are shown. Which is the missing third force? Answer: Next slide A. B. C. D. © 2015 Pearson Education, Inc.

Quick Check 4.1 The net force on an object points to the left. Two of three forces are shown. Which is the missing third force? Answer: C. Reason: The net force of the two forces points up and to the right. Using vector addition by the head-to-tail method, it will become clear that once you add the third vector given in answer C, the vertical components will cancel out and there will be a resulting net force that points to the left. A. B. C. D. © 2015 Pearson Education, Inc.

Quick Check 4.2 A ball rolls down an incline and off a horizontal ramp. Ignoring air resistance, what force or forces act on the ball as it moves through the air just after leaving the horizontal ramp? The weight of the ball acting vertically down. A horizontal force that maintains the motion. A force whose direction changes as the direction of motion changes. The weight of the ball and a horizontal force. The weight of the ball and a force in the direction of motion. Answer: A Reason: Once the ball leaves the ramp, when ignoring air resistance, the only force acting on the ball is that of gravity (weight). Much like in projectile motion, we always stated that the only acceleration was that due to gravity. This force of weight and the acceleration due to gravity both point exclusively downward. © 2015 Pearson Education, Inc.

Quick Check 4.3 A steel beam hangs from a cable as a crane lifts the beam. What forces act on the beam? Gravity Gravity and tension in the cable Gravity and a force of motion Gravity and tension and a force of motion Answer: B Reason: First identify the contact forces. In this case, the only contact force is that of tension in the rope. Then, identify the long range forces. In this case, the only one is weight (or the force due to gravity). © 2015 Pearson Education, Inc.

Quick Check 4.4 A bobsledder pushes her sled across horizontal snow to get it going, then jumps in. After she jumps in, the sled gradually slows to a halt. What forces act on the sled just after she’s jumped in? Gravity and kinetic friction Gravity and a normal force Gravity and the force of the push Gravity, a normal force, and kinetic friction Gravity, a normal force, kinetic friction, and the force of the push Answer: D Reason: There is the long range force of gravity (weight) of the bobsledder. There are also two contact forces. The first is the normal force since the person is on a surface (the surface exerts a normal force on the person). The second is kinetic friction since the person is sliding across the surface. This force opposes the person’s motion. © 2015 Pearson Education, Inc.

Quick Check 4.5 A cart is pulled to the right with a constant, steady force. How will its acceleration graph look? Answer: C Reason: Newton’s second law has shown that an object that is pulled with a constant force will experience a constant acceleration. In this case, the force is constant and so the acceleration is constant. Graph C shows such a situation where the acceleration is, indeed, not changing. A. B. C. © 2015 Pearson Education, Inc.

Quick Check 4.6 A constant force causes an object to accelerate at 4 m/s2. What is the acceleration of an object with twice the mass that experiences the same force? 1 m/s2 2 m/s2 4 m/s2 8 m/s2 16 m/s2 Answer: B Reason: Acceleration is inversely proportional to mass, meaning that as one increases, the other decreases. In this case, we double the mass, so the acceleration is halved. One half of 2 is 1 and the correct answer is then B. © 2015 Pearson Education, Inc.

Quick Check 4.7 An object, when pushed with a net force F, has an acceleration of 2 m/s2. Now twice the force is applied to an object that has four times the mass. Its acceleration will be ½ m/s2 1 m/s2 2 m/s2 4 m/s2 Answer: B Reason: ai = Fi/mi = 2  af = 2Fi/4mi = ½ Fi/mi = ½ ai = 1 Thus, the correct answer is B. © 2015 Pearson Education, Inc.

Quick Check 4.8 A 40-car train travels along a straight track at 40 mph. A skier speeds up as she skis downhill. On which is the net force greater? The train The skier The net force is the same on both. There’s not enough information to tell. Answer: B Reason: F = ma. If there is no acceleration, there is no force. In this example, the train is moving at a constant speed so it had no acceleration so its force is zero. The skier, however, is accelerating and, even though we don’t know the exact values, we know this implies there must be some force. Thus, the answer is B. © 2015 Pearson Education, Inc.

Quick Check 4.9 An object on a rope is lowered at constant speed. Which is true? The rope tension is greater than the object’s weight. The rope tension equals the object’s weight. The rope tension is less than the object’s weight. The rope tension can’t be compared to the object’s weight. Answer: B Reason: First identify the forces. In this case we have the weight pointing down and the tension from the rope pointing up. Now, determine whether or not there is a net force so you know how large the arrows must be (the magnitude). The problem states that it is moving at a constant speed. Constant speed implies no acceleration. No acceleration implies no net force. As a result, the two forces must be equal in magnitude. Therefore, the answer is B. © 2015 Pearson Education, Inc.

Quick Check 4.10 An object on a rope is lowered at a steadily decreasing speed. Which is true? The rope tension is greater than the object’s weight. The rope tension equals the object’s weight. The rope tension is less than the object’s weight. The rope tension can’t be compared to the object’s weight. Answer: A Reason: Same as last problem, but now the object is decreasing in speed. It is moving down and slowing down. Since it is slowing down, the acceleration points in the opposite direction of the motion (upward). Since there is an acceleration, there is a force and the force points in the same direction as the acceleration. Thus, there must be a net force pointing upward. The only way this happens is if the tension in the rope is greater than the object’s weight. The correct answer is A. © 2015 Pearson Education, Inc.

Quick Check 4.11 An elevator, lifted by a cable, is moving upward and slowing. Which is the correct free-body diagram? Answer: C Reason: Identify the forces. Here, we have the weight of the elevator pointing downward and the tension in the cable pointing upward. The elevator is moving up, but slowing down. This implies that the acceleration points downward. This further implies that there is a net force pointing downward, which will occur when the weight is greater than the tension. The correct answer is C. A. B. C. D. E. © 2015 Pearson Education, Inc.

Quick Check 4.12 A ball has been tossed straight up. Which is the correct free-body diagram just after the ball has left the hand? Ignore air resistance. Answer: D Reason: The ball is tossed into the air. Once it leaves the person’s hand, the only force acting upon the ball is that due to gravity; the weight of the ball. This points straight down and the answer is, thus, D. © 2015 Pearson Education, Inc. A. B. C. D.

Quick Check 4.13 A ball, hanging from the ceiling by a string, is pulled back and released. Which is the correct free-body diagram just after its release? Answer: B Reason: There are two forces acting on the ball. The contact force is that of tension, which points along the rope (up and to the right). The long range force is that of gravity which points straight down. The correct answer is B. We do not tilt axes as it is not an inclined plane problem. A. B. C. D. E. © 2015 Pearson Education, Inc.

Quick Check 4.14 A car is parked on a hill. Which is the correct free-body diagram? Answer: C Reason: There are three forces at play in this example. Two contact forces and one long range force. The long range force is that of gravity (the weight). The two contact forces are the normal force (of the surface on the car, perpendicular to the ramp), and the static friction force, which points in the direction necessary to oppose the motion (so backward, up the ramp to the left). The correct answer is C. © 2015 Pearson Education, Inc.

Quick Check 4.15 A car is towed to the right at constant speed. Which is the correct free-body diagram? Answer: D Reason: There are four forces at play in this example. Three contact forces and one long range force. The long range force is the weight of the car. The contact forces are the normal force upward, the kinetic friction to the left, and the tension in the rope to the right. It is moving at a constant speed so there is no acceleration and no net force, so the magnitudes are the same and the answer is D. © 2015 Pearson Education, Inc.

Quick Check 4.17 A mosquito runs head-on into a truck. Splat! Which is true during the collision? The mosquito exerts more force on the truck than the truck exerts on the mosquito. The truck exerts more force on the mosquito than the mosquito exerts on the truck. The mosquito exerts the same force on the truck as the truck exerts on the mosquito. The truck exerts a force on the mosquito but the mosquito does not exert a force on the truck. The mosquito exerts a force on the truck but the truck does not exert a force on the mosquito. Answer: C Reason: Newton’s third law summarizes as “for every action, there is an equal but opposite reaction. The bug will exert the same force on the truck as the truck exerted on the bug. The answer is C. © 2015 Pearson Education, Inc. 18