1. The problem statement, all variables and given/known data
A mass of 5 kg follows the potential energy shown by the equation:
[tex] U(x) = .333(x-4)^3 - \dfrac{x^2}{4} + 5[/tex]
1. Find the force on the mass at x=2
2. Describe the motion qualitatively if the mass is placed at x=4 m and released
3. With part 1, determine the max speed of the mass
4. With #1, determine where the mass will again come to rest if at all.
2. Relevant equations
mgh
1/2mv^2
3. The attempt at a solution
1. I got this pretty easily, as -3N
2. I really had no idea for this. I thought that it would eventually settle at x=5.6 m.
3. U(4)-U(5.68) = .5mv^2 so v=1.576
4. u(4)-U(5.868) = U(x_0) => x_0 = 7.162 m
Is this correct?
A mass of 5 kg follows the potential energy shown by the equation:
[tex] U(x) = .333(x-4)^3 - \dfrac{x^2}{4} + 5[/tex]
1. Find the force on the mass at x=2
2. Describe the motion qualitatively if the mass is placed at x=4 m and released
3. With part 1, determine the max speed of the mass
4. With #1, determine where the mass will again come to rest if at all.
2. Relevant equations
mgh
1/2mv^2
3. The attempt at a solution
1. I got this pretty easily, as -3N
2. I really had no idea for this. I thought that it would eventually settle at x=5.6 m.
3. U(4)-U(5.68) = .5mv^2 so v=1.576
4. u(4)-U(5.868) = U(x_0) => x_0 = 7.162 m
Is this correct?
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