OPEN RESPONSE #1:

A 45 kg child is swinging on a swing set. Positions X and Z represent the highest points of the person’s motion, and position Y represents the lowest point of the person’s motion.

• At which position does the person have maximum kinetic energy? Explain your answer.

• Draw a diagram of the child on the swing. Lable X, Y, and Z.

• Describe the energy conversion as the person travels from position X to position Y. Neglect Friction.

• The person is 1.0 m above the ground at position Y and 1.5 m above the ground at position Z. Neglecting friction, calculate the change in gravitational potential energy as the person swings from position Y to position Z. Show your calculations and include units in your answer.

• Calculate the speed of the person at position Y. Show your calculations and include units in your answer. Neglect friction.

Step 1:

Lets identify our givens (everything that we have and know about this problem).

mass= 45 kg, x and z = high points of motion, y= lowest point of motion

What formulas can we use for the first bullet point. Kinetic Energy? hmm.. look at your formula sheet if you don't know.

So now we have KE= 1/2mv^2 . We know the mass stays the same the whole time. So to have the maximum KE it has to be the spot that has maximum velocity! Which is what? When you're on a swing and you get to the highest point what happens? You stop! So you have a maximum height and minimum velocity. Which means y would have the minimum height and greatest velocity. The answer to the first bullet point is Y because of this. The child speeds up and then begins to slow. The equation for potential energy is PE=mgh. So if you have a lot of height, your PE will be great and you KE will be smaller.

Step 2:This is the diagram of the situation. This isn't too hard as it says X and Z are maximum height and the lowest high would be when the chains on the swing are straight down.

Step 3:Neglect Friction makes this third bullet much easier. Neglect just simply means ignore, so don't get stressed about this part. So picture being on a swing when you are all the way back at point x what happens as you approach y? You get faster right? You also get at a lower height where your feet might even touch the floor. So this is simple now. If the height is large at X then you have potential energy (PE=mgh), then as you speed up the PE turn to KE (1/2mv^2). Energy conversion is just changing one form of energy to another form. So don't be intidimated by the word. Conversion is just like convert. Whenever you convert something it means change.

Step 4: So this is asking you to find the potential energy (PE=mgh). We already know gravity (g=9.8 m/s^2) and the mass remains the same so m= 45 kg. Now two heights are given so we have two problems. Plug in the first height (h=1.0 m) and get your first solution. Then plug in the second height (h=1.5m) and get your second solution. The units of energy is Joules. Remember not to skip any of the questions, because you will lose points. Once you anwser each part you can check or cross it off.

Step 5: If you are calculating the speed (this is the same as velocity) then you need the Kinetic Energy formula of KE=1/2mv^2.  The value you received for PE at Z is the same value you will receive for the KE at point Y. Because the energy is completed converted to KE at the lowest height. Also the energy is all potential energy at point Z because the velocity is zero. So set KE equal to the PE value and simply do algebra. Multiply the 2 over from the 1/2 so you have 2KE= 2/2 mv^2, which is the same as 2KE= mv^2. Now divide by mass, so 2KE/m= mv^2/ m, the same as 2KE/m=v^2. The last step is to take the square root of both sides. Then you can plug in the mass of 45 kg and the Joules for KE. Then you will have your speed. Remember to include units, the units for speed it always m/s.