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Physics and Measurement Standards of Length, Mass, time and Dimensional Analysis The laws of physics are expressed in terms of basic quantities that require a clear definition. In mechanics, the three basic quantities are length (L), mass (M), and time (T). All other quantities in mechanics can be expressed in terms of these three.

In 1960, an international committee established a set of standards for length, mass, and other basic quantities. The system established is an adaptation of the metric system, and it is called the SI system of units. (The abbreviation SI comes from the system’s French name “Système Inter-national.”) In this system, the units of length, mass, and time are the meter, kilogram, and second, respectively [Kms]

Length As recently as 1960, the length of the meter was defined as the distance between two lines on a specific platinum – iridium bar stored under controlled conditions in France. This standard was abandoned for several reasons, a principal one being that the limited accuracy with which the separation between the lines on the bar can be determined does not meet the current requirements of science and technology. In the 1960s and 1970s, the meter was defined as 1 650 763.73 wavelengths of orange-red light emitted from a krypton-86 lamp. However, in October 1983, the meter (m) was redefined as the distance travelled by light in vacuum during a time of 1/299 792 458 second.

Mass The basic SI unit of mass, the kilogram (kg), is defined as the mass of a specific platinum –iridium alloy cylinder kept at the International Bureau of Weights and Measures at Sèvres, France. This mass standard was established in 1887 and has not been changed since that time because platinum–iridium is an unusually stable alloy

Time Before 1960, the standard of time was defined in terms of the mean solar day for the year 1900.2 The mean solar second was originally defined as of a mean solar day. The rotation of the Earth is now known to vary slightly with time, however, and therefore this motion is not a good one to use for defining a standard. Thus, in 1967 the SI unit of time, the second, was redefined using the characteristic frequency of a particular kind of cesium atom as the “reference clock.” The basic SI unit of time, the second (s), is defined as 9 192 631 770 times the period of vibration of radiation from the cesium-133 atom

DIMENSIONAL ANALYSIS In solving problems in physics, there is a useful and powerful procedure called dimensional analysis. Dimensional analysis makes use of the fact that dimensions can be treated as algebraic quantities. quantities can be added or subtracted only if they have the same dimensions. Furthermore, the terms on both sides of an equation must have the same dimensions. .

Let us use dimensional analysis to check the validity of this expression. The quantity x on the left side has the dimension of length L. We can perform a dimensional check by substituting the dimensions for acceleration, L/T2, and time, T, into the equation. That is, the dimensional form of the equation is The units of time squared cancel as shown, leaving the unit of length.

CONVERSION OF UNITS Sometimes it is necessary to convert units from one system to another. Conversion factors between the SI units and conventional units of length are as follows:

EXAMPLE 1.1 Analysis of an Equation Show that the expression v = at is dimensionally correct, where v represents speed, a acceleration, and t a time interval. EXAMPLE 1. 2 Analysis of a Power Law Suppose we are told that the acceleration a of a particle moving with uniform speed v in a circle of radius r is proportional to some power of r, say rn, and some power of v, say vm. How can we determine the values of n and m?

The Laws of Motion The Concept of Force Newton’s First Law and Inertial Frames Newton’s Second Law The Force of Gravity and Weight Newton’s Third Law Some Applications of Newton’s Laws Forces of Friction

Contact forces. THE CONCEPT OF FORCE In these examples, the word force is associated with muscular activity and some change in the velocity of an object. Forces do not always cause motion, however. For example, you can push (in other words, exert a force) on a large boulder not be able to move it. If the net force exerted on an object is zero, then the acceleration of the object is zero and its velocity remains constant. Contact forces.

field forces. What force (if any) causes the Moon to orbit the Earth? Newton answered this by stating that forces are what cause any change in the velocity of an object. Therefore, if an object moves with constant velocity, no force is required for the motion to be maintained. The Moon’s velocity is not constant because it moves in a nearly circular orbit around the Earth. We now know that this change in velocity is caused by the force exerted on the Moon by the Earth. field forces.

Newton’s First Law and Inertial Frames Before about 1600, scientists felt that the natural state of matter was the state of rest. Galileo was the first to take a different approach to motion and concluded that it is not the nature of an object to stop once set in motion: rather, it is its nature to resist changes in its motion. In his words, “Any velocity once imparted to a moving body will be rigidly maintained as long as the external causes of retardation are removed.” This approach was later formalized by Newton in Newton’s first law of motion: In the absence of external forces, an object at rest remains at rest and an object in motion continues in motion with a constant velocity (that is, with a constant speed in a straight line).

NEWTON’S SECOND LAW Newton’s second law answers the question of what happens to an object that has a nonzero resultant force acting on it. F1 a1 m1 F2 a2 = 2a1 (A) 2F1 (B) F1 (C) 1/2 F1 From such observations, we conclude that the acceleration of an object is directly proportional to the resultant force acting on it.

F a1 m1 a2 = 2a1 m2 (A) 2m1 (B) m1 (C) 1/2 m1 From such observations, we conclude that the acceleration of an object is inversely proportional to its mass. The acceleration of an object is directly proportional to the net force acting on it and inversely pro-portional to its mass. These observations are summarized in Newton’s second law:

Newton’s second law Unit of Force !? Thus, we can relate mass and force through the following mathematical statement of Newton’s second law The SI unit of force is the Newton, which is defined as the force that, when acting on a 1-kg mass, produces an acceleration of 1 m/s2. Unit of Force !?

In the British engineering system, the unit of force is the pound, which is defined as the force that, when acting on a 1-slug mass produces an acceleration of 1 ft/s2:

A hockey puck having a mass of 0 A hockey puck having a mass of 0.30 kg slides on the horizontal, frictionless surface of an ice rink. Two forces act on the puck, as shown in Figure. The force F1 has a magnitude of 5.0 N, and the force F2 has a magnitude of 8.0 N. Determine both the magnitude and the direction of the puck’s acceleration. Solution

The resultant force in the x direction is The resultant force in the y direction is Now we use Newton’s second law in component form to find the x and y components of acceleration: The acceleration has a magnitude of and its direction relative to the positive x axis is

NEWTON’S THIRD LAW This simple experiment illustrates a general principle of critical importance known as Newton’s third law: If two objects interact, the force F12 exerted by object 1 on object 2 is equal in magnitude to and opposite in direction to the force F21 exerted by object 2 on object 1:

In reality, either force can be labeled the action or the reaction force. The action force is equal in magnitude to the reaction force and opposite in direction. In all cases, the action and reaction forces act on different objects

why does the TV not accelerate in the direction of Fg ? What is happening is that the table exerts on the TV an upward force n called the normal force. The normal force is a contact force that prevents the TV from falling through the table and can have any magnitude needed to balance the downward force Fg