Question

A 21 kg object is acted on by a conservative force given by F = -1.0x - 6.0x^2, with F in newtons and x in meters. Take the potential energy associated with the force to be zero when the object is at x = 0. (a) What is the potential energy of the system associated with the force when the object is at x = 1.7 m? (b) If the object has a velocity of 4.0 m/s in the negative direction of the x axis when it is at x = 3.7 m, what is its speed when it passes through the origin? What are the answers to (c) (a) and (d) (b) if the potential energy of the system is taken to be -10 J when the object is at x = 0?

Answer 1

Date Now Distance = speed x time Sheed = Distance time = = 4 m/ 3.7 0.925 ч ту, spu a = Menu we conclude that a sume when barrices ongen on x-axts. when the speed estrain basses through the © Given this In when n=0 = -105 case du = - Fan l du = 1 1-10a-6:00) an - 10 0410 = (a + 6 m2 0410 = '(-3) 7 2013) - .U4 10 = 11.271 U= 11.27 - 10 Tu= 1.271 Joule

m= 21 kg F = -1.on- 6.00 onserahu force At no uso (given). ponnal @ we know that Energy U and relation between Force given hy F = - du don ON du = -F da du = (-1.on-bion an c cloc on +6.on? An 2 . [o-c(tt)r +(6) ] = [928.6 t shhit Jan U= 11. 271 Joule 6 v= 4.0 m/s in - we n-direction ostrom m Now t= 0 Displacement velocity - - 1= 3.7 3.7 40 0.925 s bus 126.0