# This is a mathematical methods and mechanics problem. Hope you can help thanks.

Posted: December 30th, 2021

A block of mass m is given an initial velocity of Mo at a ?xed origin 0 and it began toslide on a rough horizontal surface. At a position x from 0, it has a velocity of v. Take the magnitude of the acceleration due to gravity to be g and the coef?cient of slidingfriction to be ,u. (a) De?ne an appropriate coordinate axis, draw a force diagram of the block andwrite down the vector form of all forces. (5 marks) (b) Apply Newtonian mechanics and present the equation of motion for the block.(3 marks) (c) Show that the distance travelled by the block from the origin 0 is given by (4 marks) ((1) For no = 2 ms’1 and p! = 0.02, calculate the distance travelled by the block whenit comes to a stop. (2 marks) Now consider the effect of air resistance. The same block of mass m is given an initialvelocity of no at a ?xed origin 0 and it began to slide on a rough holizontal surface.When sliding, the block now expeliences air resistance of magnitude A7152. (e) Apply Newtonian mechanics and solve an expression the distance travelled bythe block from the origin 0, in terms of m, am, y, k, v and g.(7 marks}

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