OpenStax University Physics Volume I Unit 1: Mechanics Chapter 5: Newton’s Laws of Motion University Physics Volume I Unit 1: Mechanics Chapter 5: Newton’s Laws of Motion Conceptual Questions 1. What properties do forces have that allow us to classify them as vectors? Solution Forces are directional and have magnitude. 2. Taking a frame attached to Earth as inertial, which of the following objects cannot have inertial frames attached to them, and which are inertial reference frames? (a) A car moving at constant velocity (b) A car that is accelerating (c) An elevator in free fall (d) A space capsule orbiting Earth (e) An elevator descending uniformly Solution Because (b), (c), and (d) all involve accelerating reference frames, they are noninertial reference frames; (a) and (e) involve constant velocity, so they are inertial reference frames. 3. A woman was transporting an open box of cupcakes to a school party. The car in front of her stopped suddenly; she applied her brakes immediately. She was wearing her seat belt and suffered no physical harm (just a great deal of embarrassment), but the cupcakes flew into the dashboard and became “smushcakes.” Explain what happened. Solution The cupcake velocity before the braking action was the same as that of the car. Therefore, the cupcakes were unrestricted bodies in motion, and when the car suddenly stopped, the cupcakes kept moving forward according to Newton’s first law. 4. Why can we neglect forces such as those holding a body together when we apply Newton’s second law? Solution Internal forces on the constituent components of a system cancel each other out to produce a net force of zero and hence do not contribute to the motion of the system. 5. A rock is thrown straight up. At the top of the trajectory, the velocity is momentarily zero. Does this imply that the force acting on the object is zero? Explain your answer. Solution No. If the force were zero at this point, then there would be nothing to change the object’s momentary zero velocity. Since we do not observe the object hanging motionless in the air, the force could not be zero. 6. What is the relationship between weight and mass? Which is an intrinsic, unchanging property of a body? Solution Classically, mass is a constant and intrinsic property of matter, whereas weight is the manifestation of gravity acting on a mass. 7. How much does a 70-kg astronaut weight in space, far from any celestial body? What is her mass at this location? Solution Page 1 of 28 OpenStax University Physics Volume I Unit 1: Mechanics Chapter 5: Newton’s Laws of Motion The astronaut is truly weightless in the location described, because there is no large body (planet or star) nearby to exert a gravitational force. Her mass is 70 kg regardless of where she is located. 8. Which of the following statements is accurate? (a) Mass and weight are the same thing expressed in different units. (b) If an object has no weight, it must have no mass. (c) If the weight of an object varies, so must the mass. (d) Mass and inertia are different concepts. (e) Weight is always proportional to mass. Solution e 9. When you stand on Earth, your feet push against it with a force equal to your weight. Why doesn’t Earth accelerate away from you? Solution The force you exert (a contact force equal in magnitude to your weight) is small. Earth is extremely massive by comparison. Thus, the acceleration of Earth would be incredibly small. To see this, use Newton’s second law to calculate the acceleration you would cause if your weight is 600.0 N and the mass of Earth is 6.00× 1024 kg . 10. How would you give the value of in vector form? Solution Since always acts vertically downward, we write it this way: . 11. Identify the action and reaction forces in the following situations: (a) Earth attracts the Moon, (b) a boy kicks a football, (c) a rocket accelerates upward, (d) a car accelerates forward, (e) a high jumper leaps, and (f) a bullet is shot from a gun. Solution a. action: Earth pulls on the Moon, reaction: Moon pulls on Earth; b. action: foot applies force to ball, reaction: ball applies force to foot; c. action: rocket pushes on gas, reaction: gas pushes back on rocket; d. action: car tires push backward on road, reaction: road pushes forward on tires; e. action: jumper pushes down on ground, reaction: ground pushes up on jumper; f. action: gun pushes forward on bullet, reaction: bullet pushes backward on gun. 12. Suppose that you are holding a cup of coffee in your hand. Identify all forces on the cup and the reaction to each force. Solution force of hand on cup, reaction: force of cup on hand; force of Earth on cup (that is, weight), reaction: force of cup on Earth 13. (a) Why does an ordinary rifle recoil (kick backward) when fired? (b) The barrel of a recoilless rifle is open at both ends. Describe how Newton’s third law applies when one is fired. (c) Can you safely stand close behind one when it is fired? Solution a. The rifle (the shell supported by the rifle) exerts a force to expel the bullet; the reaction to this force is the force that the bullet exerts on the rifle (shell) in opposite direction. b. In a recoilless rifle, the shell is not secured in the rifle; hence, as the bullet is pushed to move forward, the shell is pushed to eject from the opposite end of the barrel. c. It is not safe to stand behind a recoilless rifle. 14. A table is placed on a rug. Then a book is placed on the table. What does the floor exert a normal force on? Page 2 of 28 OpenStax University Physics Volume I Unit 1: Mechanics Chapter 5: Newton’s Laws of Motion Solution only the rug 15. A particle is moving to the right. (a) Can the force on it to be acting to the left? If yes, what would happen? (b) Can that force be acting downward? If yes, why? Solution a. Yes, the force can be acting to the left; the particle would experience deceleration and lose speed. B. Yes, the force can be acting downward because its weight acts downward even as it moves to the right. 16. In completing the solution for a problem involving forces, what do we do after constructing the free-body diagram? That is, what do we apply? Solution We apply Newton’s first law if the forces are balanced or Newton’s second law if the system is accelerating. 17. If a book is located on a table, how many forces should be shown in a free-body diagram of the book? Describe them. Solution two forces of different types: weight acting downward and normal force acting upward 18. If the book in the previous question is in free fall, how many forces should be shown in a free-body diagram of the book? Describe them. Solution only one force: weight acting downward Problems 19. Two ropes are attached to a tree, and forces of and are applied. The forces are coplanar (in the same plane). (a) What is the resultant (net force) of these two force vectors? (b) Find the magnitude and direction of this net force. Solution a. ; b. the magnitude is Fnet =11 N , and the direction is θ =63 ° 20. A telephone pole has three cables pulling as shown from above, with , , and . (a) Find the net force on the telephone pole in component form. (b) Find the magnitude and direction of this net force. Solution Page 3 of 28 OpenStax University Physics Volume I Unit 1: Mechanics Chapter 5: Newton’s Laws of Motion a. ; b. Fnet = 316.0 N and θ =−°71.6 from the positive x-axis 21. Two teenagers are pulling on ropes attached to a tree. The angle between the ropes is 30.0° . David pulls with a force of 400.0 N and Stephanie pulls with a force of 300.0 N. (a) Find the component form of the net force. (b) Find the magnitude of the resultant (net) force on the tree and the angle it makes with David’s rope. Solution a. ; b. at θ =12.8 ° from David’s rope 75.0 ˆˆ 150.0 ˆˆ 22. Two forces of F1 =( ij − ) N and F2 =( ij − ) N act on an object. Find the third 2 2 force that is needed to balance the first two forces. Solution 23. While sliding a couch across a floor, Andrea and Jennifer exert forces and on the couch. Andrea’s force is due north with a magnitude of 130.0 N and Jennifer’s force is 32° east of north with a magnitude of 180.0 N. (a) Find the net force in component form. (b) Find the magnitude and direction of the net force. (c) If Andrea and Jennifer’s housemates, David and Stephanie, disagree with the move and want to prevent its relocation, with what combined force should they push so that the couch does not move? Solution ˆˆ a. Fnet =95.0 ij + 283 N ; b. 299 N at 71° north of east; ˆˆ c. FFDS=−=−+ net (95.0 i 283 j) N 24. Andrea, a 63.0-kg sprinter, starts a race with an acceleration of 4.200 m/s2 . What is the net external force on her? Solution 2 Fnet = ma = (63.0 kg)(4.200 m/s )= 265 N 25.