Chapter 4: Linear Kinetics, Force and Newton’s Laws of Motion

Conceptual Questions

4.1 Forces

  1. What properties do forces have that allow us to classify them as vectors?
    Solution: Forces are directional and have magnitude.
  2. &Which statement is correct?
    (a) Net force causes motion.
    (b) Net force causes change in motion. Explain your answer and give an example.
  3. &Describe a situation in which the net external force on a system is not zero, yet its speed remains constant.
  4. &A system can have a nonzero velocity while the net external force on it is zero. Describe such a situation.
  5. &A rock is thrown straight up. What is the net external force acting on the rock when it is at the top of its trajectory? 

4.2 Newton’s First Law

  1. 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
  2. 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.
  3. &How are inertia and mass related?

4.3 Newton’s Second Law

  1. Why can we neglect forces such as those holding a body together when we apply Newton’s second law?
  2. 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.
  3. &Which statement is correct?
    (a) Net force causes motion.
    (b) Net force causes change in motion. Explain your answer and give an example.
  4. &Describe a situation in which the net external force on a system is not zero, yet its speed remains constant.
  5. &A system can have a nonzero velocity while the net external force on it is zero. Describe such a situation.
  6. &A rock is thrown straight up. What is the net external force acting on the rock when it is at the top of its trajectory?
  7. &(a) Give an example of different net external forces acting on the same system to produce different accelerations.
    (b) Give an example of the same net external force acting on systems of different masses, producing different accelerations.
    (c) What law accurately describes both effects? State it in words and as an equation.
  8. &If the acceleration of a system is zero, are no external forces acting on it? What about internal forces? Explain your answers.
  9. &If a constant, nonzero force is applied to an object, what can you say about the velocity and acceleration of the object?
  10. &The gravitational force on the basketball in the figure below is ignored. When gravity is taken into account, what is the direction of the net external force on the basketball—above horizontal, below horizontal, or still horizontal?
    (a) A basketball player pushes the ball with the force shown by a vector F toward the right and an acceleration a-one represented by an arrow toward the right. M sub one is the mass of the ball. (b) The same basketball player is pushing a car with the same force, represented by the vector F towards the right, resulting in an acceleration shown by a vector a toward the right. The mass of the car is m sub two. The acceleration in the second case, a sub two, is represented by a shorter arrow than in the first case, a sub one.

4.4 Newton’s Third Law

  1. 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
    (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.
  2. &Describe a situation in which one system exerts a force on another and, as a consequence, experiences a force that is equal in magnitude and opposite in direction. Which of Newton’s laws of motion apply?
  3. &An American football lineman reasons that it is senseless to try to out-push the opposing player, since no matter how hard he pushes he will experience an equal and opposite force from the other player. Use Newton’s laws and draw a free-body diagram of an appropriate system to explain how he can still out-push the opposition if he is strong enough.

4.6 Mass and Weight

  1. What is the relationship between weight and mass? Which is an intrinsic, unchanging property of a body?
  2. How much does a 70-kg astronaut weight in space, far from any celestial body? What is her mass at this location?
    Solution: 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.
  3. 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.
  4. 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 [latex]6.00\,×\,{10}^{24}\,\text{kg}[/latex].
  5. How would you give the value of [latex]\overset{\to }{g}[/latex] in vector form?
  6. To simulate the apparent weightlessness of space orbit, astronauts are trained in the hold of a cargo aircraft that is accelerating downward at g. Why do they appear to be weightless, as measured by standing on a bathroom scale, in this accelerated frame of reference? Is there any difference between their apparent weightlessness in orbit and in the aircraft?
    Solution: The scale is in free fall along with the astronauts, so the reading on the scale would be 0. There is no difference in the apparent weightlessness; in the aircraft and in orbit, free fall is occurring.

4.7 Normal, Tension and Other Forces

  1. A table is placed on a rug. Then a book is placed on the table. What does the floor exert a normal force on?
  2. Suppose that you are holding a cup of coffee in your hand. Identify all forces on the cup and the reaction to each force.
  3. & In a traction setup for a broken bone, with pulleys and rope available, how might we be able to increase the force along the tibia using the same weight? (See the figure below) Diagram of a leg in traction.

4.8 Friction

  1. The glue on a piece of tape can exert forces. Can these forces be a type of simple friction? Explain, considering especially that tape can stick to vertical walls and even to ceilings.
  2. When you learn to drive, you discover that you need to let up slightly on the brake pedal as you come to a stop or the car will stop with a jerk. Explain this in terms of the relationship between static and kinetic friction.
    Solution: If you do not let up on the brake pedal, the car’s wheels will lock so that they are not rolling; sliding friction is now involved and the sudden change (due to the larger force of static friction) causes the jerk.
  3. When you push a piece of chalk across a chalkboard, it sometimes screeches because it rapidly alternates between slipping and sticking to the board. Describe this process in more detail, in particular, explaining how it is related to the fact that kinetic friction is less than static friction. (The same slip-grab process occurs when tires screech on pavement.)
  4. &Define normal force. What is its relationship to friction when friction behaves simply?

4.9 Drag Forces

  1. Athletes such as swimmers and bicyclists wear body suits in competition. Formulate a list of pros and cons of such suits.
    Solution: The pros of wearing body suits include: (1) the body suit reduces the drag force on the swimmer and the athlete can move more easily; (2) the tightness of the suit reduces the surface area of the athlete, and even though this is a small amount, it can make a difference in performance time. The cons of wearing body suits are: (1) The tightness of the suits can induce cramping and breathing problems. (2) Heat will be retained and thus the athlete could overheat during a long period of use.
  2. Two expressions were used for the drag force experienced by a moving object in a liquid. One depended upon the speed, while the other was proportional to the square of the speed. In which types of motion would each of these expressions be more applicable than the other one?
  3. Why can a squirrel jump from a tree branch to the ground and run away undamaged, while a human could break a bone in such a fall?

4.10 Elasticity: Stress and Strain

  1. The elastic properties of the arteries are essential for blood flow. Explain the importance of this in terms of the characteristics of the flow of blood (pulsating or continuous).
  2. What are you feeling when you feel your pulse? Measure your pulse rate for 10 s and for 1 min. Is there a factor of 6 difference?
  3. Examine different types of shoes, including sports shoes and thongs. In terms of physics, why are the bottom surfaces designed as they are? What differences will dry and wet conditions make for these surfaces?
  4. Would you expect your height to be different depending upon the time of day? Why or why not?
  5. Would you expect a large or small stress to be required to deform a spider web? Why is this elasticity an important feature for a spider web?
  6. Explain why pregnant women often suffer from back strain late in their pregnancy.
  7. An old carpenter’s trick to keep nails from bending when they are pounded into hard materials is to grip the center of the nail firmly with pliers. Why does this help?
  8. When a glass bottle full of vinegar warms up, both the vinegar and the glass expand, but vinegar expands significantly more with temperature than glass. The bottle will break if it was filled to its tightly capped lid. Explain why, and also explain how a pocket of air above the vinegar would prevent the break. (This is the function of the air above liquids in glass containers.)

4.11 Problem-Solving Strategies

  • To solve problems involving Newton’s laws of motion, follow the procedure described:
    1. Draw a sketch of the problem.
    2. Identify known and unknown quantities, and identify the system of interest. Draw a free-body diagram, which is a sketch showing all of the forces acting on an object. The object is represented by a dot, and the forces are represented by vectors extending in different directions from the dot. If vectors act in directions that are not horizontal or vertical, resolve the vectors into horizontal and vertical components and draw them on the free-body diagram.
    3. Write Newton’s second law in the horizontal and vertical directions and add the forces acting on the object. If the object does not accelerate in a particular direction (for example, the x-direction) then [latex]{F}_{\text{net}\phantom{\rule{0.25em}{0ex}}x}=0[/latex]. If the object does accelerate in that direction, [latex]{F}_{\text{net}\phantom{\rule{0.25em}{0ex}}x}=\text{ma}[/latex].
    4. Check your answer. Is the answer reasonable? Are the units correct?

4.12 Further Applications of Newton’s Laws

  1. To simulate the apparent weightlessness of space orbit, astronauts are trained in the hold of a cargo aircraft that is accelerating downward at [latex]g[/latex]. Why will they appear to be weightless, as measured by standing on a bathroom scale, in this accelerated frame of reference? Is there any difference between their apparent weightlessness in orbit and in the aircraft?
  2. A cartoon shows the toupee coming off the head of an elevator passenger when the elevator rapidly stops during an upward ride. Can this really happen without the person being tied to the floor of the elevator? Explain your answer.

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Introduction to Biomechanics Copyright © 2022 by Rob Pryce is licensed under a Creative Commons Attribution 4.0 International License, except where otherwise noted.

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