Answers to selected problems for Chapter 2 are found here.
| Exercise 7. |
To pull a wagon across a lawn at a constant velocity, you must exert a steady force. Reconcile this with Newton's First Law, which states that constant velocity indicates no force. In this example, the wagon is in contact with the lawn, and there is friction involved in the contact. (There is also friction with the air, but this is much less important.) Friction provides a force opposed to the direction of motion -- such forces are called drag by engineers -- and so a countervailing force must be supplied to keep the wagon moving. The moving wagon is in dynamic equilibrium, but it wouldn't be if no motive force was supplied. |
| Exercise 11. | A common saying goes, "It's not the fall that hurts; it's the sudden stop." Translate this into Newton's Laws of Motion. What we feel is force that changes or counteracts our state of motion (Newton's First Law). If we are falling, no counteracting force is acting on us. But when we strike a barrier, it strikes back! (Newton's Third Law) The force of the barrier pushing back on us hurts in proportion to our speed of impact (Newton's Second Law). |
| Exercise 17. | What is the net force on an apple that weighs 1 N when you hold it at rest above your head? What is the net force on it when you release it? The net force when you are holding it is zero. The 1 N gravitational force ("weight") is opposed by an equal supporting force exerted by your hand. But when you release the apple, the net force on it is its 1 N weight, no longer counteracted by a supporting force. (There's also air friction, but that's more-or-less negligible unless you drop the apple from a very great height.) |
| Exercise 27. | If a Mack truck and a motorcycle have a head-on collision, upon which vehicle is the impact force greater? Which vehicle undergoes the greater change in its motion? Explain. Two colliding objects exert equal and opposite forces on each other (Newton's Third Law). However, acceleration experienced by an object is inversely related to its mass: the smaller the mass, the larger the acceleration for a given force (pp. 49-50). Therefore the motorcycle will undergo a much greater change in its motion than the truck. |
| Exercise 34. | Free fall is motion in which gravity is the only force acting. Is a skydiver who has reached terminal speed in free fall? Is a satellite circling the earth above the atmosphere in free fall? No, the skydiver is not in free fall. The definition of terminal velocity is the state in which the force of air friction equals the falling object's weight. So instead the skydiver is in dynamic equilibrium between the forces of gravity and friction. However, the satellite is in free fall. It is responding to gravity freely, with no opposing frictional force. The fact that it circles the Earth is a consequence of the independence of horizontal and vertical motion; it is in fact traveling in a ballistic curve, just like a cannonball! |
| Exercise 36. | You tell your friend that the acceleration of a skydiver decreases as falling progresses. Your friend then asks if this means the skydiver is slowing down. What is your response? NO. Acceleration means a change in speed. Positive values mean speed is increasing, and "decreasing acceleration" would have to go through zero to negative values for the skydiver to begin slowing down. As long as acceleration is positive, the skydiver is still speeding up, just at a slower rate of increase as acceleration decreases. |
| Problem 7. | A rocket of mass 100,000 kg undergoes an acceleration of 2 m/s2. Calculate the force being developed by the rocket engines. Force = mass × acceleration (p. 50); 1 N is defined as the force required to accelerate 1 kg of mass by 1 m/s2. Therefore the force being exerted by the rocket engines is 100,000 kg × 2 m/s2 = 200,000 N. |