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N76 [4]
4 years ago
5

A certain spring is found not to obey Hooke’s law; it exerts a restoring force Fx(x)=−αx−βx2 if it is stretched or compressed, w

here α=60.0N/m and β=18.0N/m2. The mass of the spring is negligible. (a) Calculate the potential-energy function U(x) for this spring. Let U = 0 when x = 0. (b) An object with mass 0.900 kg on a frictionless, horizontal surface is attached to this spring, pulled a distance 1.00 m to the right (the +x-direction) to stretch the spring, and released. What is the speed of the object when it is 0.50 m to the right of the x = 0 equilibrium position?
Physics
1 answer:
Masteriza [31]4 years ago
4 0

Answer:U(x) = 30x^2 +6x^3

V^2=8.28m/s

Explanation:The law of conservation of energy is given by K1+U1= K2+U2 ...eq 1

Kinetic energy K.E= 1/2 mv^2

Restoring force function F(x)= -60x - 18x^2

But F(x)= -dU/dx

dU(x)=-F(x)dx

Integrating U(x)= -integral F(x)dx + U(0)

Substituting, we get

U(x) = - integral(-60x-18x^2)dx+U(0)

U(x)= 30x^2+6x^3+U(0)

U=0 at x=0

Therefore U(x)= 30x^2+6x^3

b) Given : x1=1.00m,x2= 0.50m ,V1=0, V2=?

Substituting into eq (a)

U1= 30(1.00)^2+6(1.00)^3=36J

Using x2=0.5 into eq(a)

U2=30(0.50)^2+6(0.50)^3=8.25J

Object at rest K1=0

0+36=K2+8.25

K2=27.75J

Given; m =0.900kg, V2=?

27.75=1/2×0.900×V2^2

V2= SQRT(2×27.75)/0.81

V2= 8.28m/s

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A rock is thrown upward from level ground in such a way that the maximumheight of its flight is equal to its horizontal rangeR.
Snowcat [4.5K]
A) The vertical component of velocity v is taking the rock to a height

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5 0
3 years ago
A solid block of copper, which is a good conductor, has a cavity in its interior. Within the cavity, insulated from the conducto
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Answer:

The charge on the outer surface of the block = -5.00 nC

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The point charge within the cavity will induce a charge equal in magnitude and opposite in sign on the inside cavities of the copper block.

Charge of the point charge = 3.00 nC

Charge induced on the inner surface of the Copper block's cavity = -3.00 nC

Since the charge on a conductor should usually be neutral, the charge on the inner surface causes a charge equal in magnitude and also opposite in sign on the outer surface of the block; that is, 3.00 nC.

But this block already has an excess charge of -8.00 nC (which resides on the surface because excess charge for conductors reside on the surface of the conductors)

So, net charge on the outer surface of the Copper block = -8.00 + 3.00 = -5.00 nC.

Hope this Helps!!!

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3 years ago
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sesenic [268]

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