Chapter 08, Problem 038 can travel only along an x axis under the influence of a

Question

Chapter 08, Problem 038 can travel only along an x axis under the influence of a conservative The fiqure shows a plot of potential eneroy U versus position x of a 0.230 kg partide that here U forms a-potential hr of height" force. The graph has these values: UA-9.00 , Uc·20.0 ] and UD-24.0 J. The partide is released at the point w Us-12.0 3, with kinetic energy 5.00 J. What is the speed of the partide at (a)x-3.50 m and (b)x 6.50 m? what is the position of the right side and (d) the left side? 6 (a) Number (b) Number (c) Number (6) Number Units Units Units

Explanation / Answer

a)

At t = 3.5 m, it is at potential energy = UA

So, it loses UB - UA = 12 - 9 = 3 J of PE

So, it must gain 3J of KE during that interval

So, KE = 0.5*mv^2 = 3

So, 0.5*0.23*v^2 = 3

So, v = 5.11 m/s <------- answer

b)

At x = 6.5 m, it loses Ub = 12 J of PE

So, KE = 12

So, 0.5*0.23*v^2 = 12

So, v = 10.2 m/s <------- answer

c)

Similarly for the turning point on the right :

y = (24/1)*x = 12

So, x = 0.5 m

So, turing point on the right = 7 + 0.5 = 7.5 m <------ answer

d)

For position of turing point , the point must have potential = Uc = 12 J

So, on the right side , for the point y = 20 - ((20 - 9)/2)*x = 12

So, x = 1.45 m

So, the turning point o the left is x = 1 +1.45 = 2.45 m <--------- answer

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