Question

A body of mass m= 1 kg is moving along the x-axis. Its potential energy is given by the function

U(x)=2(x2−1)2
Note: The units were dropped for the numbers in the equation above. You should note that 2 would carry units of J⋅m−4 and 1 would carry units of m2



a) What is the x -component of the force associated with the potential energy given by U(x) ? Give an expression in terms of x.

Fx(x)=


b) At what positive value of x ( x>0) in m, does the potential have a stable equilibrium point ?

x=


c) Suppose the body starts with zero speed at x=1.5 m. What is its speed (in m/s) at x=0 m and at x=−1 m?

v(x=0)=


v(x=−1)=

Answer 1

a) Fx(x)= -8*x*(x^2-1)

b). x=1

c) v(x=-1)= sqrt(6)

Answer 2

c) v(x=0)= 1.5

Answer 3

please could you help me with the 3rd(2nd part) one and the 4th one..plzzz help