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**Unformatted text preview: **FIRST YEAR PHYSICS FIRST YEAR PHYSICS PHYS141 LECTURER: Dr. Carey Freeth Rm 4.110 Ph. 02 42214798 Email: [email protected] We will now develop some techniques for solving problems where the forces acting on a body are not all constant. Consider Frst, a simple situation of a constant force acting on an object. The work that force F does on the object in moving it from x 1 to x 2 is deFned as W= ¡ cos ! " x or W = ¡ x " x since ¡ x = ¡ cos ! . Note: It is the component of the force in the direction of the motion that does the work. Work is positive if the motion is in the same direction as the force and negative if it is in the opposite direction. __________________________________________________ Units of work Force x distance # > [newtons] [meter]-> Nm-> [joule] __________________________________________________ The above equation can be simpli¡ed by writing in the form of a scaler or dot product. __________________________________________________ Scaler Product W = F " x cos ! = F . " x . is called a scaler product since this type of product of the two vectors F and " x , gives a scaler. In general C = A . B where A . B = AB cos ! and ! is the angle between A and B . __________________________________________________ If the force is not constant but depends on x then we calculate F . " x for each position or value of x and sum all of these to give the total work. Such a process is called integration in calculus and written as W = r F .d r x x 1 x 2 ! . " x F 1 F 2 W = F 1 " x+ F 2 " x + …….. Hence work is simply the area under the Force vs displacement curve. This can be extended to three dimensions by realising that its only the component of the force in the direction of the displacement that contributes to the work. The component of the force perpendicular to the direction of motion does not effect the speed, but can change the direction of the object. Hence: and W = r F .d r s = 1 2 !...

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