First, find the velocity of the falling body which has fallen 16 ft. A body falls 16 ft. in _one_ second. In this time it gains a velocity of 32 ft. per second. Now using the formula for kinetic energy _K.E._ = _wv_²/(2_g_), we have _K.E._ = 100 × 32 × 32/(2 × 32) = 1600 ft.-lbs. as before. The formula, _K.E._ = _wv_²/(2_g_), may be derived in the following manner: The kinetic energy of a falling body equals the work done in giving it its motion, that is, _K.E._ = _w_ × _S_, in which, _w_ = the weight of the body and _S_ = the distance the body must fall freely in order to acquire its velocity. The distance fallen by a freely falling body, _S_, = 1/2_gt_² = _g_²_t_²/(2_g_) (Art. 98, p. 111). Now, _v_ = _gt_ and _v_² = _g_²_t_². Substituting for _g_²_t_², its equal _v_², we have _S_ = _v_²/(2_g_). Substituting this value of S in the equation _K.E._ = _w_ × _S_, we have _K.E._ = _wv_²/(2_g_). Since the kinetic energy of a moving body depends upon its mass and velocity and not upon the _direction_ of motion, this formula may be used to find the kinetic energy of any moving body. Mass and weight in such problems may be considered numerically equal. =Important Topics= 1. Work defined. 2. Work units, foot-pound, kilogram-meter, erg. 3. Energy defined. 4. Kinds of energy, potential and kinetic. =Problems= 1. How much work will a 120-lb. boy do climbing a mountain 3000 ft. high? Should the vertical or slant height be used? Why? 2. In a mine 4000 kg. of coal are lifted 223 meters: how much work is done upon the coal? What is the kind and amount of energy possessed by the coal? 3. A pile driver weighs 450 lbs. It is lifted 16 ft. How much work has been done upon it? What kind and amount of energy will it have after falling 16 ft. to the pile? 4. A train weighing 400 tons is moving 30 miles per hour. Compute its kinetic energy. (Change its weight to pounds and velocity to feet per second.) 5. What would be the kinetic energy of the train in problem 4 if it were going 60 miles per hour? If it were going 90 miles per hour? How does doubling or trebling the speed of an object affect its kinetic energy? How does it affect its momentum? 6. What is the kinetic energy of a 1600-lb. cannon ball moving 2000 ft. per second? 7. Mention as many kinds of mechanical work as you can and show how each satisfies the definition of work. 8. A pile driver weighing 3000 lbs. is lifted 10 ft. How much work is done upon it? 9. If the pile driver in problem 8 is dropped upon the head of a pile which meets an average resistance of 30,000 lbs., how far will one blow drive it? 10. A 40 kg. stone is placed upon the top of a chimney 50 meters high. Compute the work done in kilogram-meters and foot-pounds.