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giving a kinetic energy of less than 5 joules. Where did the other 14 joules go The problem is that this velocity is the average velocity across the entire fall, most of which is spent going really slow. The kinetic energy would need to be calculated for the nal velocity of the ball when it hit. This is trickier, and is not explored here. Sorry.
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1. Statics is the study of the forces on objects as they just sit there. Dynamics is more concerned with forces of objects in motion. Note that kinematics is also the study of motion. They go hand in hand: kinematics of motion, dynamics of the forces behind the motion. 2. Cutting paper uses shearing forces, and scissors are often called shears. Crushing a grape uses compression force and breaking a string involves tension. Examinations also include tension, but of a di erent sort. 3. The vertical part of the motion is the part that ghts gravity. This is calculated as the sine of the angle: v sin 10 v 0:17 So as we push the robot up the ramp, it is ghting 17% of gravity s force, or an acceleration of 1.67 m/s2. Now that you know the acceleration ghting the climb of the robot, what else can you calculate, assuming you also know the weight of the robot 4. Your knee, like your elbow, is the fulcrum for a second-class lever. Your ankle, however, is the fulcrum in the center of the rst-class lever that is your foot. 5. 25 teeth, each taking 0.125 inch, uses up 3.125 inches total. This would be the circumference of the gear, so the gear s radius is just about a half inch: c 2  r 3:125 6:283 r r 3:125 6:283
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The big gear has a diameter of 4.97 inches giving a radius of 2.485 inches. The circumference is then: c 2  2:485 c 15:61 Leaving room for 125 teeth. Okay, 124.9 teeth. The math, as shown, rounds the numbers, losing a bit of accuracy. The mechanical advantage is then 5:1 or 1:5, depending on how you look at it. Note that this is essentially the same as 15.61:3.125, the relative circumferences of the gears. For that matter, it s also the same as the ratio of the diameters, 0.994:4.97.
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