7 Work and Energy 50m×9.8m/s2 ×0.10 = 7.0m/s. Suppose a constant force Fx acts in the +x−direction and causes an object to move a distance of ∆x. The work-done by the force is defined as W =fx∆x. The SI unit of work is joule (i.e., 1 newton-metre). If the force makes an angle θ with the direction of motion (the x-axis here), the work-done by F is W =Fx∆x=Fcosθ∆x. Example: A man drags a heavy log across level ground by attaching a cable from the log to a bulldozer. The cable is inclined upward from horizontal at an angle of 20◦. The cable exerts a constant force of 2000 N while pulling the log 16 m. How much work is done in dragging the log? Solution: W =Fcosθ∆x=(2000)(cos20◦)(16) = 3.0×104J. Note: 1. If the displacement ∆x is written as a vector, we can write: W =F·∆x 2. The area of a force-displacement graph gives the workdone by the force. (44) An important example of a non-constant force is the force exerted by a spring or a rubber band. Suppose a mass is attached to one end of a spring and placed on a frictionless horizontal surface. The other end of the spring is attached to a fixed point. If the mass is then displaced an amount x from its equilibrium position, the spring exerts a force F on it, where F =−kx, (45) where k is the spring constant. The minus sign indicates that this spring force is a restoring force. The workdone in stretching a spring distance x is x x W = F dx = 0 W =1 2 0 kx2. kxd
