1) A 60 foot length of steel chain weighing 10 pounds per foot is hanging from the top of a building. How much work is required to pull half of it to the top?2) A bucket weighing 1000 pounds is to be lifted from the bottom if a shaft is 20 feet deep. The weight of the cable used to hoist it is 10 pounds per foot. How much work is done lifting the bucket to the top of the shaft?3) A spring has natural length of 1 meter. A force of 24N is used to stretch the spring to a length of 1.8 meters.a) Find the force constant kb) How much work will it take to stretch the spring 2m beyond its natural length?c) How far will a 45N force stretch the spring?Please show work so that i can understand how you got your answer because i have the answers just don't know how it's done thank you! =)
1) W = Fs (where Work = Force * Distance changed) The force F in this case is the Weight of the object. This is given as 10 pounds/foot *60 foot = 600 pounds S = change in distance. This is given as 1/2 the total length of steel = 1/2 * (60) = 30 feet So W = Fs = 600 * 30 = 18,000 Joules 2) Again W = Fs There are TWO objects here so we need to sum the two work equations together. In other words, there are two forces and distances involved. The first force F1 is the Weight of bucket,given as 1000 pounds. Change in distance = 20 feet; So Work 1 = F1*s = 1000*20 = 20,000 Joules The second force F2 is the Weight 2 of the cable, which is 10 pounds/ft * 20 ft = 200 pounds. Work 2 = F2 * s = 200*20 = 4,000 Joules Thus, Work 1 + Work 2 = 20,000 + 4,000 = 24,000 Joules The weight of the object * distance changed = Work done to lift bucket = 1000 * 20 = 20,000 Joules 3a) F of spring = kx (where k = force constant, and x = change in length of spring) So 24 = k (1.8) or k = 24/1.8 = 13.33 N/m b) W = Fs = 24*2 = 48 Joules c) F = kx From above, k = 13.33 N/m Given F = 45N So 45 = 13.33 * x x = 45/13.33 = 3.38 meters
