![]() Solve: The arithmetic is identical to that of Example 3.2-the force on 0.102 kg of mass (which is about 4 oz in common English units) is 1.00 N in other words, one newton is just about the weight of a small apple here on Earth ! Perhaps, this will help you mentally imagine the magnitude of a force stated in newtons. How: Equation (3.5) with g c = 1 (since we are using SI units). Know: Newton's Second Law applies using MKS units. Need: Weight in newtons on a mass of 0.102 kg accelerated at 9.81 m/s 2. What is the weight in newtons of a mass of 0.102 kg? It is convenient to give this set of units a unique new name (mainly to keep from having to write the combined mass times acceleration units for every force), and in the SI system, the force unit is called the newton (abbreviated N). 3 The unit of force must then simply be equivalent to the units of mass times the units of acceleration. ![]() The ratio F 1/ m 1 a 1 was chosen so that its numerical value is exactly “1” and so that it effectively has no (i.e., ) dimensions. The SI system is somewhat similar to the slug system with the choice for the constant of proportionality g c being both easy and logical. Its disadvantage is that you have little “feel” for the size of a slug. Its obvious advantage is that Newton's Second Law constant of proportionality g c is exactly 1, so the law can be written in the familiar form of F = ma, with the stipulation that mass m is in slugs and the acceleration is in ft/s 2. In fact, the slug system is still preferred in the United States in some engineering fields. G c = m 1 a 1 F 1 = 1 slug × ft lbf × s 2 Hence the two components of force are of the same size, as long as the pipe diameter is constant round the bend, and the resultant force on the bend will be outwards and at 45° to each of the two arms of the pipe. The liquid is brought to rest in the original direction and accelerated from rest up to full speed in the final direction. The calculation for such a situation is similar to that for the curved vane above except that pipe bends are usually right angles and so the working is easier. In practical terms this is important because the supports for the pipe must be designed to be strong enough to withstand this force. Therefore if a liquid flows along a pipeline which has a bend in it then a considerable force can be generated on the pipe by the liquid even though the liquid may keep the same speed throughout. This means that a force will be required to change the direction of a flowing liquid, just as it is required to change the speed of the liquid. ![]() Velocity is a vector quantity and so it has direction as well as magnitude. ![]() ![]() Newton's second law relates to the forces caused by changes in velocity. Bill Bolton, in Mechanical Engineering Systems, 2001 Forces on pipe bends And indeed, as illustrated in Figure, the same net external force applied to a car produces a much smaller acceleration than when applied to a basketball.Richard Gentle. In other words, the larger the mass (the inertia), the smaller the acceleration produced by a given force. Now, it also seems reasonable that acceleration should be inversely proportional to the mass of the system. It is a tremendous simplification not to have to consider the numerous internal forces acting between objects within the system, such as muscular forces within the child’s body, let alone the myriad of forces between atoms in the objects, but by doing so, we can easily solve some very complex problems with only minimal error due to our simplification Once the system of interest is chosen, it is important to identify the external forces and ignore the internal ones. The techniques are the same as for the addition of other vectors, and are covered in the chapter section on Two-Dimensional Kinematics.) This proportionality states what we have said in words- acceleration is directly proportional to the net external force. (The net external force is the vector sum of all external forces and can be determined graphically, using the head-to-tail method, or analytically, using components. ![]()
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