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Fundamental Forces • We have talked about a lot of different kinds of forces. • Gravitational, friction, normal, fluid resistance, tension… • Are these all actually different in nature? • Four fundamental forces (we think): • Gravitational • Electromagnetic • Strong • Weak • All interactions arise through one of these fundamental forces. • All of the interactions we have dealt with so far were electromagnetic or gravitational. Chapter 5 Summary Applying Newton’s Laws • Statics: 𝑭=0 • Dynamics: 𝑭 = 𝑚𝒂 • Friction • Kinetic friction: 𝑓k = 𝜇k 𝑛 • Static friction: 𝑓s ≤ 𝜇s 𝑛 • Rolling resistance: 𝑓r = 𝜇r 𝑛 • Fluid resistance: 𝑓 = 𝑘𝑣 or 𝑓 = 𝐷𝑣 2 • Terminal velocity: 𝑣𝑡 = • Circular Motion • Fundamental forces 𝑚𝑔 𝐷 Chapter 6 Outline Work and Kinetic Energy • Work and energy • Conservation of energy • Kinetic Energy • Work-energy theorem • Work with varying forces • Power • Fundamental forces Work and Kinetic Energy • In everyday conversation, work would be any activity that requires some effort. • In physics, work is something that is done to change the energy of an object. • Energy can take many forms. • Consider the case of applying a force on a body. • As we saw last chapter, the body will accelerate. • Its kinetic energy, or energy of motion, will increase. • If we apply the force over a longer distance, we increase the kinetic energy more. Work and Forces • If we apply a constant force, 𝐹, over some distance 𝑠, in the same direction as the force, the work done is: 𝑊 = 𝐹𝑠 • What are the units for work? • Force is measured in newtons, and distance in meters. • Work is therefore measured in newton-meters. • We call this a joule. • 1J= 1N∙m Work and Forces Not Aligned with Displacement • If the force is not applied in the same direction as the displacement, only the component of the force aligned with the displacement contributes to the work done. • We only consider the component of the force parallel to the displacement multiplied with the magnitude of the displacement. • This is simply the dot product of the force and the displacement. 𝑊 = 𝑭 ∙ 𝒔 = 𝐹𝑠 cos 𝜙 Sign of Work • Work is a scalar. It does not indicate a direction, but its sign is still quite important. • The sign of the work done on an object depends on the direction of both the force and the displacement. • If the force and the displacement are in the same direction, the work done by the force on the body is positive. • It is crucially important to indicate who/what is doing the work and who/what the work is done upon. Total Work • In general, there are often more than one force acting on an object. • The total work done on the object depends on the net force and the displacement of the object. • Multiple forces/bodies can do different, sometimes opposing, amounts of work on the body. Work Example Kinetic Energy • When a force is applied to a body, it causes an acceleration. • A force applied over a distance, as we have said is the definition of work. • This changes the kinetic energy of the object. • How can we relate work done to change in kinetic energy? Kinetic Energy • When a force is applied to a body, it causes an acceleration. • A force applied over a distance, as we have said is the definition of work. • This changes the kinetic energy of the object. • How can we relate work done to change in kinetic energy? Work-Energy Theorem • Kinetic energy is: 𝐾 = 12𝑚𝑣 2 • The net work done on a body is equal to the change in kinetic energy. • This is the work-energy theorem. 𝑊tot = 𝐾2 − 𝐾1 = Δ𝐾 Work-Energy Example