Do 1 of the 2 problems. A force of 34 pounds is required to hold a spring stretc

Question

Do 1 of the 2 problems. A force of 34 pounds is required to hold a spring stretched 2.3 feet beyond its natural length. How much work (in foot-pounds) is done in stretching the spring from its natural length to 4.2 feet beyond its natural length? It took 34 Joules Of work to stretch a spring from its natural length of 14 meters beyond its natural length. What is the force (in Newtons) that holds the spring stretched at the same distance 16 meters? Do 1 of the 2 problems Find the x-coordinate x, or the y-coordinate y. of the centroid of the region bounded by the given curves. Y = -x + 2, 0 lessthanorequalto x lessthanorequalto 2 y = e^2x, y = 0,x = 0,x = 2

Explanation / Answer

1)

1)F=kx

k=F/x

k=34/2.3

work done = [0 to 4.2] (34/2.3)x dx

work done = [0 to 4.2] (34/2.3)(1/2)x2

work done = (34/2.3)(1/2)4.22 -0

work done = 130.4 pond feet

2)

work=(1/2)kx2

34=(1/2)k 142

k=34*2/142

k=17/49

x =16 m

F=kx

F=(17/49)*16

F=5.55 Newton

2)

1)y =-x+2 ,0<=x<=2

My =[0 to 2] x(-x+2) dx

My =[0 to 2] (-x2+2x) dx

My =[0 to 2] (-(1/3)x3+x2)

My =(-(1/3)23+22)-0

My =4/3

Mx =[0 to 2] (1/2)(-x+2)2 dx

Mx =[0 to 2] -(1/2)(1/3)(-x+2)3

Mx =[-(1/2)(1/3)(-2+2)3 ]-[-(1/2)(1/3)(-0+2)3 ]

Mx =0+(4/3)

Mx =4/3

area A=2

x coordinate=My/A=(4/3)/2= 2/3

y coordinate=Mx/A=(4/3)/2= 2/3

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