Problem statementSolution video |

**DISCUSSION THREAD**

**Discussion and hints:**

Recall the following *f**our-step plan* outline in the lecture book and discussed in lecture:

**Step 1: FBD**

Draw a free body diagram of the system made up of P. Which, if any, forces do non-conservative work on this system? Can you justify this from the FBD?

**Step 2: Kinetics (work/energy equation)**

Write down the work energy equation for P. Recall that the potential energy in a spring is 0.5*k*Δ^{2}, where Δ is the stretch/compression in the spring. Δ is *NOT* equal to the length of the spring. Recall that the spring is unstretched at position 2.

**Step 3: Kinematics**

What kinematics do you need here?

**Step 4: Solve**

Solve your work/energy equation for the speed of P at position 2.

Any questions??

Does the spring being unstretched also mean it is not compressed?

Yes.

I went through the problem and found the answer without using kinematics. I just found that setting up the force/energy equation gives only 1 unknown (velocity at 2), and I solved for it. Does this seem like the right approach? Also, I said that the spring force does positive work while the gravitational force does negative work as it is below my datum. Does this sound correct, too?

You probably used kinematics without realizing it. In order to determine change in length of the spring, you needed to use kinematics (geometry of motion).

My recommendation is to always include spring forces and gravitational forces in the potential energy terms, rather than in work. With that, you know that the potential energy of the spring is ALWAYS non-negative, and that the potential energy due to gravity depends on whether the center of mass of the body is above or below the datum line.

Are we always constrained to set the datum line at the first position, or can we set it at the second position in this specific problem to avoid anything being below it?

You are free to use ANY horizontal plane as the datum. Choose one that simplifies your calculations.

Would the normal force count as non-conservative for the purposes of my U calculations?