L7-s1,9 Physics 114 – Lecture 7 Chapter 4 Dynamics: Newton’s Laws of Motion We now investigate why bodies undergo motion. Why do bodies accelerate? They do so under the action of applied unbalanced forces. What is a force? Examples of a force – friction, gravity, a force exerted by a spring, etc. Forces can be exerted by an inanimate object, e.g., by a hammer striking a nail

L7-s2,9 Physics 114 – Lecture 7 §4.1 Force Pushing or pulling an object, lawn mower, wheelbarrow, etc., requires an applied force, magnitude and direction. Magnitude – one way is to use a calibrated spring scale Force also has an associated direction

L7-s3,9 Physics 114 – Lecture 7 §4.2 Newton’s First Law of Motion Relationship between force and motion? Aristotle ( B.C.) believed that a force was necessary to maintain a body in constant motion on a horizontal surface. Aristotle maintained that the greater the speed the greater the required force Galileo, in about 1630, about 2000 years later, disputed this suggestion, arguing that it was just as natural for a body to move with constant velocity – magnitude and direction – as it was to be at rest. Note that = 0 is a reasonable value for a constant velocity

L7-s4,9 Physics 114 – Lecture 7 Consider a hockey puck moving across a rough surface with some initial velocity. How far does it travel before coming to rest – note that it travels in a straight line? Now consider the puck moving over the surface to which some lubricant has been applied. → It will travel further before coming to rest. Now consider a puck moving across smooth ice. → It will travel still further.

L7-s5,9 Physics 114 – Lecture 7 What is the factor that has been influencing these changes? We now recognize this factor to be a progressive reduction in the force of friction between the body and the surface. Galileo considered that, in principle, friction between the surface and the puck might be eliminated altogether. In such a situation no unbalanced force acted on the body, which would then maintain its motion with constant velocity, until it was disturbed, i.e., an unbalanced force was then applied to the body to change its state of motion.

L7-s6,9 Physics 114 – Lecture 7 Newton’s First Law Any object continues in its state of rest, or in a state of uniform velocity – in a straight line – provided that no unbalanced force acts on it Inertial Reference Frames Reference frames, in which Newton’s First Law holds, are known as inertial reference frames

L7-s7,9 Physics 114 – Lecture 7 §4.3 Mass Mass? Newton used the term to describe the quantity of matter in a body. It is better used as a measure of the inertia of a body. The larger the mass, the larger is the force required to give it with a particular acceleration. Units of m? in the SI system the unit of mass is the kilogram – kg. Note that mass and weight are distinct quantities

L7-s8,9 Physics 114 – Lecture 7 §4.4 Newton’s Second Law of Motion is the net or total force acting on the body Notice that this is a vector equation where a vector, the acceleration, is multiplied by a scalar, the mass. Thus the force and the acceleration act in the same direction We see that if the mass is held constant then the acceleration is proportional to the force and in the same direction as the force

L7-s9,9 Physics 114 – Lecture 7 If the force is held constant then the magnitude of the acceleration is inversely proportional to the mass, but the force and the acceleration still act in the same direction Units of force? In the SI system the units of force are the newton ≡ kg m/s 2 Notice that Newton’s First Law is a special case of Newton’s Second Law, because velocity = 0 or v = constant both require acceleration = 0 → F = ma = 0 Lets look at some examples Note – → F x = ma x, F y = ma y