a 251 kg crate hangs from the end of a rope of length L = 15.0 m. You push horiz
ID: 2012965 • Letter: A
Question
a 251 kg crate hangs from the end of a rope of length L = 15.0 m. You push horizontally on the crate with a varying force to move it distance d = 4.07 m to the side. (a) What is the magnitude of when the crate is in this final position? During the crate's displacement, what are (b) the total work done on it, (c) the work done by the gravitational force on the crate, and (d) the work done by the pull on the crate from the rope? (e) Knowing that the crate is motionless before and after its displacement, use the answers to (b), (c), and (d) to find the work your force does on the crate.Explanation / Answer
Mass of the crate is m = 251 kg Length of the rope is L = 15.0m force to move a distance is d = 4.07m a ) To hold the crate in the final situation F must have same magnitude is sin = 4.07 m / 15.0m = 15.74 degrees vertical component of the tension supports aganist the weights T cos = mg T = 251 kg * 9.8 m/s^2 / cos 15.74 = 2555.6 N magnitude of when the crate is in this final position is F = 2555.6 N *sin 15.74 = 693.2 N b) There is no change in kinetic energy so Net work done is zero c ) The work done by the gravitational force is W_g = F_g * d = - mg h h = L ( 1- cos) = 15.0m ( 1- cos 15.74) = 0.56m W_g = - 251 kg * 9.8m/s^2 * 0.56m = -1383.5 N d ) Tension vector is every where perpendicular to the direction of motion so the work done is zero e ) From the above three parts Net force is F = - W_g = 1383.5 NRelated Questions
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