Physics Homework- Please help me this question and show me step by step. Thank y

Question

Physics Homework- Please help me this question and show me step by step. Thank you so much

Suppose the following function describes the potential energy of a point mass (m=1 kg) at various locations in the xy plane:

suppose the following function describes the potential energy of a point mass (m=1 kg) at various locations in the xy plane: U(x,y)=x2-y2 + 34 (Units omitted; you may assume [x], [y] = m and [U] = J.) c.) From there, the object now is given an ever-so-slight nudge in the -y direction Use your force function to show that the object will always feel a force that points along the -y axis from then on. when the object arrives at y=-5 m, find: the energy stored by the object: its speed m/s

Explanation / Answer

Fx = - dU/dx

= -2x

Fy = -dU/dy

= 2y

this gives when object move in - y direction then it will experiance a force in the -y direction as well

b)

assume initially object is at (0 , 0) so initially U = 34 J

adn as we pust it in -y direction it will experiance a force in - y direction so it accelerate along -y axis

so when object is at (0, -5)

U = - 25 + 34 = 9 J

so loss in U = gain in KE

34 - 9 = mv^2 / 2

v = 7.07 m/s

enery will remain constant = 34 J = initial energy of object

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