Lecture 6 > Forces > Newton's Laws > Normal Force, Weight (Source: Serway; Giancoli) 1
Dynamics > Knowing the initial conditions of moving objects can predict the future motion of the said objects. > In dynamics, the cause of an object's motion is studied. > Forces acting of objects with mass causes them to change their motion. + The relation between force and changes in motion are described by Newton's laws. + A reference frame is a mathematical model used to describe these relations (similar to an x-y plane). http://physics.nhn.ou.edu/~jeffery/astro/ial/ial_005.shtml 2
Forces > The main cause of a body's change in motion is termed a force. + It is commonly represented as a push or a pull exerted on an object. + It's measured in units of newtons (N = kg-m/s 2 ) or dynes (dyne = g-cm/s 2 ). A force of one newton will make a 1-kg object accelerate at 1 m/s 2. A person holding a 10-kg sack of rice feels a force of ~100 N on the hand. + As a vector quantity, the force is exerted along a given direction. imgarcade.com 3
Forces contd. > Different types of forces exist depending on their nature or description: + Contact forces that appear when two or more bodies touch. + Field forces that act over a distance, such as the gravitational pull between the heavenly bodies. + Other field forces such as electricity & magnetism, weak forces in decaying atomic nuclei, and strong forces keeping atomic nuclei together. > Aside from causing objects to move, forces can also deform and reshape bodies, such as metal bending during a car crash. cliparts.co wikiwand.com imgarcade.com 4
First Law of Motion > An object sliding across a surface stops after it has traveled a certain distance. + Making the surface smoother lets the object travel farther before stopping. + If the surface is ideally smooth, then the object would slide forever. + In an ideal state with no countering force, then bodies would likewise slide on forever. v > First Law: Bodies initially at rest or in motion persist in their state if no net force acts on the body. + Net force = sum of all forces acting on the body + No net force = either no force or all the forces acting cancel each other out; the push and the pull balance each other. F net = F= 0 v(t)= 0 or v(t)= v 0 (at rest) (constant velocity) 5
First Law of Motion contd. > The first law illustrates the tendency for bodies to remain in their state of motion or rest; this tendency is called inertia. + The heavier the object, the more inertia it has. A moving bowling ball is more difficult to stop than a moving golf ball. + Closely linked to inertia is the mass. It measures how much an object resists changing its motion: the more massive the object, the more difficult it is to change its motion for a given net force. + Mass is measured in the SI unit of kilogram and the imperial unit of slug. > Since the law requires that bodies retain their motion unless a net force is present, it does not hold in certain cases such as a car suddenly stopping. + Thus, an inertial reference frame is defined such that if the first law is valid in such a frame (or cartesian system), then the said reference frame is inertial. 6
Second Law of Motion > The second law describes how bodies move if a net force is present. + The body's acceleration is directly proportional to the net force acting on it: strong force, greater acceleration. + The acceleration is also inversely proportional to the mass: a massive object is difficult to accelerate. + The direction of the acceleration is parallel to the net force on the body. > Second Law: The acceleration of a body is directly proportional to the net force acting on the body and is parallel to the same. F a= net = F m m a x = F x m x-acceleration due to net force along the x-axis a y = F y m y-acceleration due to net force along the y-axis 7
Second Law of Motion contd. > Force is measured in units of newton (1 N = 1 kg-m/s 2 ) + To keep a 10-kg sack of rice from falling, a person needs to exert about 100 N of force. + It's equivalent to the pound in the US system: 100 N = 22.5 lb > Ex. An 2.00-kg object is pulled by a 5.00-N force to the +x-axis and a 2.50-N force to the x-axis. What will the acceleration of the object be? F x =2.50 N,+ x axis 2.50 N 5.00 N a x =1.25 m/ s 2 Σ F x = 2.50 N a x = 1.25 m/s 2 8
Third Law of Motion > The first and second laws showed how the presence or absence of a net force affects the motion of a body. + Its absence leaves the body to continue in its state of motion. + Its presence changes the body's motion. > The third law relates how two bodies affect each other through the forces that they exert on one another. F BA F AB A B 9
Third Law of Motion contd. > Third Law: The force Body A exerts on Body B is equal to but opposite the force exerted by Body B on Body A. A F BA F AB B F BA = F AB F BA + F AB =0 > Note that these are two DIFFERENT forces acting on two DIFFERENT bodies. 10
Normal Force & Weight > Consider an object on a frictionless floor: + Gravity pulls it down. This pull is called the weight. + It remains at rest vertically; law of inertia requires that the gravitational force be countered by an opposite force of equal magnitude. + The force must be directed upward from the floor surface (normal) and have an equal magnitude to the gravitational force. a y = 0 F y = 0 N Upward Force = Downward Force F g = W = mass x acc. due to gravity = m g > Thus, a normal force acts on bodies on surfaces keeping them from falling through the surface. 11
Tension > Consider a an object hanging from a cord fixed to the ceiling (e.g. chandelier): + Assume that the cord is massless & does not stretch. + At all points on the cord, a tension is present, keeping it taut. It has the same strength at all points on the string. + The 3 rd law of motion relates the string tension to the forces on the hanging object and the ceiling. 3 rd Law Pull on ceiling by cord Pull on cord by ceiling 1 st Law Pull on object by cord Tension Hanging object Weight 3 rd Law Pull on cord by object 12
Weighing Scales > The tension is also responsible for the way weighing scales function. + For hanging scales, it responds to the tension provided by the object being weighed. + For regular scales, the role of the tension is done by the normal force. + In an accelerating elevator, this causes the body to weigh more when it goes up and weigh less when it goes down. N, body at rest Sum of Vertical Forces: Σ F y = N F g = ma Thus, F g = mg Force on scale by body 1 st Law N, acc. body a N = F g + ma = mg + ma N = m (g + a) > mg By the 3 rd Law, Force on scale = N, acc. body > N, body at rest 3 rd Law F g a Larger scale reading when the body accelerates upward; body feels heavier going up. 13
Weighing Scales contd. > The tension is also responsible for the way weighing scales function. + For hanging scales, it responds to the tension provided by the object being weighed. + For regular scales, the role of the tension is done by the normal force. + In an accelerating elevator, this causes the body to weigh more when it goes up and weigh less when it goes down. N, acc. body a Sum of Vertical Forces: Σ F y = N F g = ma Thus, N = F g ma = mg ma N = m (g a) < mg By the 3 rd Law, Force on scale = N, acc. body < N, body at rest a = g When the cord is cut, the body is in free fall; its acceleration is g. N = m (g a) = m (g g) = 0 Then, Force on scale = N, acc. body = 0 F g a Body feels lighter going down. A falling body is weightless. 14
Summary > Dynamics studies the causes of a body's motion. > The Laws of Motion govern how the presence or absence of force act on different bodies and show how bodies exert forces on each other. > Weight is the force of gravity acting on a body; the normal force of a surface pushes against a body on it. > Tension on a cord keeps a hanging object attached to it. a x = F x m F net = F= 0 v(t)= 0 or a y = F y m F BA = F AB v(t)= v 0 15