KINETICS OF A PARTICLE: FORCE AND ACCELERATIONKinetics is the study of relations between unbalanced forces and the changes in motion they produce.This topic requires that we combine our knowledge of two previously learned parts of mechanics,namely, the properties of forces that we developed in our earlier study of statics, and the kinematics ofparticle motion that we just covered. With the aid of Newton’s second law of motion, we are now readyto combine these two topics and prepare for the solution of engineering problems involving force, massand motion.Newton’s Three Laws of Motion:First Law: A particle at rest, or moving in a straight line with a constant velocity will remain in this stateprovided the particle is not subjected to an unbalanced force.Second Law: A particle acted by an unbalanced force F experiences an acceleration a that has the samedirection as the force and a magnitude that is directly proportional to the force.Third Law: The mutual forces of action and reaction between two particles are equal, opposite, andcollinear. The first and third laws were used extensively in developin g concepts of STATICS. Although these laws are also considered in DYNAMICS, Newton’s second law of motion forms the basis for most of this study, since this laws relates the accelerated motion of a particle to forces that act on it.If the mass of the particle m, Newton’s second law of motion may be written mathematical form as: F = maThis equation, which is referred to as the equation of motion, is one of the most important equations inmechanics.UNITS: In SI units, the units of force (Newtons, N) are derived by Newton’s second law from base unitsof mass (kilograms, kg) times acceleration (meter per second squared, m/s2). Thus, N = kg-m/s2.
Mass and WeightMass is a property of matter by which we can compare the response of one body with that of another. Itis an absolute quantity since the measurement of mass can be made at any location.The weight of a body, however, is not absolute since it is measured in a gravitational field, and hence itsmagnitude depends on where the measurement is made. W = mgBy comparison with F = ma, we term g the acceleration of gravityUNITS: In SI system, if the body has a mass m (kg) and is located at a point where the acceleration togravity is g (m/s2), then the weight is expressed in Newtons as W = mg. In a particular, if the body islocated at “standard location,” the acceleration due to gravity is g = 9.81 m/s2.The Equation of MotionWhen more than one force acts on a particle, the resultant force is determined by a vector summationof all the forces, for this more general case, the equation of motion may be written as: ΣF = maExample 1:A horizontal force of 10-N is applied to a 4-kg block that is at rest on a perfectly smooth, level surface.Find the speed of the block and how far it has gone after 6s.
Example 2:The 50-kg crate shown rests on a horizontal plane for which the coefficient of friction is µ=0.30, if thecrate is subjected to a 400-N towing force, determine the velocity of the crate in 3s starting from rest.
Example 3:A loaded elevator whose total mass is 800 kg is suspended by a cable whose maximum permissibletension is 20,000N. What is the greatest upward acceleration possible for the elevator under thesecircumstances?
Example 4:The figure shows a 12-kg block, A, which hangs from a string that passes over a pulley and is connectedat its other end to a 30 kg block, B, which rest in a table with coefficient of friction of µ = 0.30. Find theaccelerations of the two blocks under the assumption that the string is massless and the pulley ismassless and frictionless. What is the tension in the string?
Example 5:The figure shows the same two blocks, A and B, suspended by a string on either side of a massless,frictionless pulley. Find the accelerations of the two blocks and the tension in the string. Mass A = 12 kgand mass B = 30 kg.
Example 6:The 100-kg block A shown in the figure is released from rest. If the masses of the pulleys and the chordare negligible, determine the speed of the 20-kg block B in 2s.