You and your bicycle have combined mass 80.0 kg. When you reach the base of a bridge, you are traveling along the road at 5.00 m/s (?Fig. P6.74?). At the top of the bridge, you have climbed a vertical distance of 5.20 m and slowed to 1.50 m/s. Ignore work done by friction and any inefficiency in the bike or your legs. (a) What is the total work done on you and your bicycle when you go from the base to the top of the bridge? (b) How much work have you done with the force you apply to the pedals? Fig. P6.74
Solution 78P Step 1 of 5: Here we need to calculate the work done on the bicycle and me to go from base to top of bridge using the mass of the bicycle including me m= 80 kg, with initial speed at base v i = 5 m/s and final speed at the top of bridge is v =1.5 f/s which is at a height h= 5.2 m from ground. Given data, Mass, m= 80 kg Initial speed, v i 5 m/s Final speed, v =f1.5 m/s Height, h= 5.2 m To find, (a) Total work done in moving to the top of bridge, W= (b) Total work done on the pedal in moving to the top of bridge, W= Step 2 of 5: (a) W hat is the total work done on you and your bicycle when you go from the base to the top of the bridge The total work done from work energy theorem is given by the change in kinetic energy. W=KE W=KE KE f i 1 2 Using KE= mv 2 W= mv mv2 1 2 2 f 2 i 1 2 2 W= m(2 v f i Step 3 of 5: Substituting m= 80 kg, v =i5 m/s and v = 1f5 m/s 1 2 2 W= (82 kg)[(1.5 m/s) (5 m/s ) ] W= (82 kg)[ 22.75] W= -910 J Therefore, the total work done on the bicycle and me while moving from base to top of bridge is found to be - 910 J.