(10%) Problem 4: The potential energy of a particle as a function of position is

Question

(10%) Problem 4: The potential energy of a particle as a function of position is given as U(x)=Ax2 + Bx+C, where U will be in joules when x is in meters. The constants A, B, and C are given below. Randomized Variables A 2.5 J/m2 B-5.5 J/m C#6.6 J 50% Part (a) Input an expression for the x-component of the force as function of position F(x). Grade Summary Deductions 100% 0% 100% Deductions Potential 7 8 9 4 5 6 Attempts remaining: 17 (0% per attempt) tailed viesw 0 Submit Hint Hits: 0% deduction per hint. Hints remaining: 1 Feedback: 0%deduction per feedback. 50% Part (b) what is the force on this particle, in newtons, at x-42 cm?

Explanation / Answer

given equation is

U ( x ) = Ax2 + Bx + C

where A = 2.5 J/m2 , B = 5.5 J/m , C = 6.6 J

then writing the values in the equation is

U ( x ) = 2.5 x2 + 5.5 x + 6.6

Part a )

by doing the differentiation we can find the x - component

then

F ( x ) = dU ( x ) / dx = d ( 2.5 x2 + 5.5 x + 6.6 ) / dx

F ( x ) = 5 x + 5.5

Part b )

at x = 42 cm

x = 0.42 m

5 x + 5.5 = F ( x )

F ( x ) = 5 X 0.42 + 5.5

F ( x ) = 2.1 + 5.5

F ( x ) = 7.6 N

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