A certain spring found not to obey Hooke's law exerts a restoring force Fx(x) = —ax — /3x2 if it is stretched or compressed, where a = 60.0 Him and /3 = 18.0 HIM2. The mass of the spring is negligible. (a) Calculate the potential-energy func-tion 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 at-tached 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?

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

b) v1=7.9 m/s

Explanation:

a) the potential energy function is equal to:

when U(x)=0 and x=0

c=0

substituting the values we have to:

b) the speed of the object is equal to:

if x1=1 m, x2=0.5 m and m=0.9 kg

Clearing v1:

v1=7.9 m/s

explanation: magnetic pole, region at each end of a magnet where the external magnetic field is strongest. the south-seeking pole, or any pole similar to it, is called a south magnetic pole. unlike poles of different magnets attract each other; like poles repel each other.

energy stored in the capacitor= 9.72 x 10⁻⁴ j

explanation:

the energy stored in the capacitor is given by

e= 1/2 c v²

e= energy stored

c= capacitance= 1.5 µc= 1.5 x 10⁻⁶f

v= potential difference=36 v

so energy stored= e= 1/2 (1.5 x 10⁻⁶) (36)²

energy stored= 9.72 x 10⁻⁴j