Accelerating along a Racetrack A road race is taking place along the track shown in the figure . All of the cars are moving at constant speeds. The car at point F is traveling along a straight section of the track, whereas all the other cars are moving along curved segments of the track. Test Your Understanding 3.4: Circular Motion An object moves around a horizontal circle at constant speed. Circular Launch A ball is launched up a semicircular chute in such a way that at the top of the chute, just before it goes into free fall, the ball has a centripetal acceleration of magnitude 2 . Exercise 3.36 A railroad flatcar is traveling to the right at a speed of 13.0 relative to an observer standing on the ground. Someone is riding a motor scooter on the flatcar . Exercise 3.41: Crossing the River I A river flows due south with a speed of 1.0 . A man steers a motorboat across the river; his velocity relative to the water is 3.4 due east. The river is 860 wide. Exercise 3.42: Crossing the River II A river flows due south with a speed of 2.0 . A man steers a motorboat across the river. The river is 800 wide. Multiple Choice Question - 3.20 A Push or a Pull? Learning Goal: To understand the concept of force as a push or a pull and to become familiar with everyday forces. A force can be simply defined as a push or a pull exerted by one object upon another. Although such a definition may not sound too scientific, it does capture three essential properties of forces: Each force is created by some object. Each force acts upon some other object. The action of a force can be visualized as a push or a pull. Since each force is created by one object and acts upon another, forces must be described as interactions. The proper words describing the force interaction between objects A and B may be any of the following: "Object A acts upon object B with force ." "Object A exerts force upon object B." "Force is applied to object B by object A." "Force due to object A is acting upon object B." One of the biggest mistakes you may make is to think of a force as "something an object has." In fact, at least two objects are always required for a force to exist. Each force has a direction: Forces are vectors. The main result of such interactions is that the objects involved change their velocities: Forces cause acceleration. However, in this problem, we will not concern ourselves with acceleration--not yet. Some common types of forces that you will be dealing with include the gravitational force (weight), the force of tension, the force of friction, and the normal force. It is sometimes convenient to classify forces as either contact forces between two objects that are touching or as long-range forces between two objects that are some distance apart. Contact forces include tension, friction, and the normal force. Long-range forces include gravity and electromagnetic forces. Note that such a distinction is useful but not really fundamental: For instance, on a microscopic scale the force of friction is really an electromagnetic force. In this problem, you will identify the types of forces acting on objects in various situations. First, consider a book resting on a horizontal table. Now consider a different situation. A string is attached to a heavy block. The string is used to pull the block to the right along a rough horizontal table. Now consider a slightly different situation. The same block is placed on the same rough table. However, this time, the string is disconnected and the block is given a quick push to the right. The block slides to the right and eventually stops. The following questions refer to the motion of the block after it is pushed but before it stops. Newton's 1st Law Learning Goal: To understand Newton's 1st law. Newton's Principia states this first law of motion: An object subject to no net force maintains its state of motion, either at rest or at constant speed in a right line. This law may be stated as follows: If the sum of all forces acting on an object is zero, then the acceleration of that object is zero. Mathematically this is just a special case of the 2nd law of motion, when , prompting scholars to advance the following reasons (among others) for Newton's spelling it out separately: This expression only holds in an inertial coordinate system--one that is not accelerating--and this law really says you have to use this type of coordinate system (i.e., Newton's laws won't work inside an accelerating rocket ship.) This was a direct challenge to the Impetus theory of motion, described as follows: A mover, while moving a body, impresses on it a certain impetus, a certain power capable of moving this body in the direction in which the mover set it going, whether upwards, downwards, sideways or in a circle. By the same amount that the mover moves the same body swiftly, by that amount is the impetus that is impressed on it powerful. It is by this impetus that the stone is moved after the thrower ceases to move it; but because of the resistance of the air and the gravity of the stone, which inclines it to move in a direction opposite to that towards which the impetus tends to move it, this impetus is continually weakened. Therefore the movement of the stone will become continually slower, and at length, the impetus is so diminished or destroyed that the gravity of the stone prevails over it and moves the stone down towards its natural place. A. C. Crombie, Medieval and Early Modern Science> This theory is sometimes called the Animistic theory of motion since it envisions a "life force" being associated with motion. Newton's 1st law is often very difficult to grasp because it contradicts various common-sense ideas of motion that they have acquired from experinece in everyday life. For example, unnaccounted for forces like friction might cause a ball rolling on the playground to eventually stop, even though no obvious forces seem to be acting. When studying Newtonian mechanics, it is best to remember this as two laws: If the net force (i.e., sum of all forces) acting on an object is zero, the object will keep moving with constant velocity (which may be zero). If an object is moving with constant velocity (not speed), that is, with zero acceleration, then the net force acting on that object must be zero. Complete the following sentences to see if you can apply these ideas. Exercise 4.1 Two forces have the same magnitude . Exercise 4.2 Instead of using the x- and y-axes of Figure 4.8 to analyze the situation of Example 4.1 in the textbook, use axes rotated 37.0 counterclockwise, so the y-axis is parallel to the force = 250 . = 50 and = 120 . Exercise 4.4 A man is dragging a trunk up the loading ramp of a mover's truck. The ramp has a slope angle of 20.0 , and the man pulls upward with a force whose direction makes an angle of 30.0 with the ramp .
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