POWER THE RATE AT WHICH WORK IS BEING DONE POWER • THE RATE OF DOING WORK • WORK = FORCE * DISTANCE IS Power Work / time Power Fd / t Power Force velocity SO WHAT IS THE UNIT FOR POWER? Joules/sec or Watts 1 watt is the power produced by a force of 1N moving an object 1ms-1 CALCULATE & COMPARE POWER • DURING THE ASCENT PHASE OF A REP OF THE BENCH PRESS, TWO LIFTERS EACH EXERT AN AVERAGE VERTICAL FORCE OF 1000 N AGAINST A BARBELL WHILE THE BARBELL MOVES 0.8 M UPWARD. BUT EACH TAKES A DIFFERENT AMOUNT OF TIME. CALCULATE THE POWER OF EACH. LIFTER A: 0.50 SECONDS LIFTER B: 0.75 SECONDS CALCULATE & COMPARE POWER LIFTER A LIFTER B TABLE OF VARIABLES TABLE OF VARIABLES F = 1000 N F = 1000 N D = 0.8 M T = 0.50 S Fd t 1000 N 0.8m Power 0.50 s 800 J Power 1600 w 0.50 s Power D = 0.8 M T = 0.75 S Fd t 1000 N 0.8m Power 0.50 s 800 J Power 1067 w 0.75s Power POWER ON A STATIONARY BIKE P Fd / t GIVEN A FORCE OF 3N AND DISPLACEMENT OF 6M PER REVOLUTION, WHAT IS THE POWER PER MINUTE IF A REVOLUTION TAKES 1 SEC? P Fd rev / min P 18 Nm *60 / min P 1080 Nm / min P 1080 J / min RUNNING UP STAIRS • DURING THE POWERHOUSE LAB, JEROME RUNS UP THE STAIRS, ELEVATING HIS 102 KG BODY A VERTICAL DISTANCE OF 2.29 METERS IN A TIME OF 1.32 SECONDS AT A CONSTANT SPEED. A. DETERMINE THE WORK DONE BY JEROME IN CLIMBING THE STAIR CASE. B. DETERMINE THE POWER GENERATED BY JEROME. RUNNING UP STAIRS • DURING THE POWERHOUSE LAB, JEROME RUNS UP THE STAIRS, ELEVATING HIS 102 KG BODY A VERTICAL DISTANCE OF 2.29 METERS IN A TIME OF 1.32 SECONDS AT A CONSTANT SPEED. A. W = 102 * 10 * 2.29 = 2335.8J B. 2335.8 / 1.32 = 1769.5W • • THE SKI SLOPES AT BLUEBIRD MOUNTAIN MAKE USE OF TOW ROPES TO TRANSPORT SNOWBOARDERS AND SKIERS TO THE SUMMIT OF THE HILL. ONE OF THE TOW ROPES IS POWERED BY A 22-KW MOTOR WHICH PULLS SKIERS ALONG AN ICY INCLINE OF 14° AT A CONSTANT SPEED. SUPPOSE THAT 18 SKIERS WITH AN AVERAGE MASS OF 48 KG HOLD ONTO THE ROPE AND SUPPOSE THAT THE MOTOR OPERATES AT FULL POWER. • A. DETERMINE THE CUMULATIVE WEIGHT OF ALL THESE SKIERS. B. DETERMINE THE FORCE REQUIRED TO PULL THIS AMOUNT OF WEIGHT UP A 14° INCLINE AT A CONSTANT SPEED. C. DETERMINE THE SPEED AT WHICH THE SKIERS WILL ASCEND THE HILL. • THE SKI SLOPES AT BLUEBIRD MOUNTAIN MAKE USE OF TOW ROPES TO TRANSPORT SNOWBOARDERS AND SKIERS TO THE SUMMIT OF THE HILL. ONE OF THE TOW ROPES IS POWERED BY A 22-KW MOTOR WHICH PULLS SKIERS ALONG AN ICY INCLINE OF 14° AT A CONSTANT SPEED. SUPPOSE THAT 18 SKIERS WITH AN AVERAGE MASS OF 48 KG HOLD ONTO THE ROPE AND SUPPOSE THAT THE MOTOR OPERATES AT FULL POWER. • A. DETERMINE THE CUMULATIVE WEIGHT OF ALL THESE SKIERS. B. DETERMINE THE FORCE REQUIRED TO PULL THIS AMOUNT OF WEIGHT UP A 14° INCLINE AT A CONSTANT SPEED. C. DETERMINE THE SPEED AT WHICH THE SKIERS WILL ASCEND THE HILL. a. Weight = 48*18*10*cos(14) = 8383N b. Force = 8383 * sin(14) = 2028N c. 22000 = 2028 * v v = 22000/2028 = 10.8ms-1