Click here to purchase the entire book in PDF format. Intuitive Mechanical Reactance One last time... let's take the plate, no swimming pool, no spring attached to a concrete wall... Just a plate. However, we'll make the plate really heavy. Also, let's ignore the fact that it's hard to hold up because it's so heavy. Once again, we'll move the plate back and forth, pushing and pulling. Once again, we can see that the plate's displacement and it's velocity are the same as they were in the swimming pool and with the spring attached. However, once again, we have to think about when we're pushing and when we're pulling. Once again, let's assume that you've already started pushing and pulling - you don't have to get the whole process started. You've had the plate as close to you as it gets, and you've pushed it away until it's back to the starting point. Now, as the plate is moving forwards, you have to slow it down, otherwise it'll just keep going away because it's no heavy. So, as soon as the plate gets to the starting point, although it's moving away from you, you're pulling on it, slowing it down until it gets to its maximum displacement. When it gets there, you keep pulling so that it starts moving towards you. However, when it returns to its starting point, you have to start pushing, otherwise this heavy plate is going to hit you in the chest. So, as the plate moves towards you, you're pushing. This behaviour of displacement, velocity and your effort are shown in Figure 3.18. Figure 3.18: The relationship between the displacement of a dinner plate, its velocity and the force you have to apply to keep it moving if the plate is really heavy. Ignore the vertical scale of these three plots - just think about their shape and polarities. Positive displacement is further away from you. Positive velocity is moving away from you. Positive force is you pushing - negative indicates that you're pulling. There are three things that are interesting to note here. The first is that, just like the plate on the spring, your effort in this case is 90$^\circ$ out of phase with your effort in the swimming pool. The second is that your effort in this case is 180$^\circ$ out of phase with your effort in the case of the plate on a spring (when you were pulling on the spring, you're pushing on the heavy plate and vice versa). Finally, you should be able to decipher that you're still playing with the relationship between kinetic and potential energy in this case of the heavy plate (sounds like a Hardy Boys Mystery book - The Case of the Heavy Plate). I'll let you figure this one out.