The following are questions taken from Hammer and Elby's "Tapping epistemological resources for learning physics" (Journal of Learning Sciences).

A lab on Newton's Second Law might include such questions as:

  1. A car cruises steadily down the highway at 60 mph. Wind resistance and friction oppose the car's motion. Those backwards forces have a combined strength of 5000 Newtons. The car's engine causes a forward force to be exerted on the car. Intuitively, is this forward force less than 5000 Newtons, equal to 5000 Newtons, or greater than 5000 Newtons? Explain.
  2. In this question, we'll see if Newton's 2nd law agrees with your intuitive guess.
    1. When the car cruises at constant speed 60 mph, what is its acceleration, a? Explain your answer briefly.
    2. Therefore, according to Fnet = ma, when the car moves at constant velocity, what net force does it feel?
    3. So, is the forward force greater than, less than, or equal to the 500-newton backward force? Does this agree with your intuitive answer to question 1?
  3. Most people have--or can at least sympathize with--the intuition that the forward force must "beat" the backward force, or else the car wouldn't move. But as we just saw, when the car cruises at steady velocity, Newton's 2nd law says that the forward force merely equals the backward force; Fnet = 0. Which of the following choices best expresses your sense about what's going on here?
    1. Fnet = ma doesn't always apply, especially when there's no acceleration.
    2. Fnet = ma applies here. Although common sense usually agrees with physics formulas, Fnet = ma is kind of an exception.
    3. Fnet = ma applies here, and disagrees with common sense. But we shouldn't expect formulas to agree with common sense.
    4. Fnet = ma applies here, and appears to disagree with common sense. But there's probably a way to reconcile that equation with intuitive thinking, though we haven't yet seen how.
    5. Fnet = ma applies here. It agrees with common sense in some respects but not in other respects.
  4. Explain your view in a few sentences.
A lab on Newton's Third Law might include:
  1. A truck rams into a parked car. The truck is twice as massive.
    1. Intuitively, which is larger during the collision: the force exerted by the truck on the car, or the force exerted by the car on the truck?
    2. If you guessed that Newton's 3rd law does not apply to this collision, briefly explain what makes this situation different from when Newton's 3rd law does apply.
  2. (Experiment) To simulate this scenario, make the "truck" (a cart with extra weight) crash into the "car" (a regular cart). The truck and car both have force sensors attached. Do whatever experiments you want, to see when Newton's 3rd law applies. Write your results here, continuing on back if needed.
  3. Most people have the intuition that the truck pushes harder on the car than vice versa, because the car "reacts" more strongly during the collision. But Newton's 3rd law applies. So, should we toss that intuition into the trash and just accept that Newton's 3rd law violates common sense? Well, before taking that step, let's clarify the "reaction" intuition to see if we can reconcile it with Newton's 3rd law.
    1. During the collision, suppose the truck loses 5 m/s of speed. Keeping in mind that the car is half as heavy as the truck, how much speed does the car gain during the collision? Visualize the situation, and trust your instincts.
    2. Does your part (a) answer agree with Newton's 3rd law? To find out, we'll need to do a few calculations. During the collision, the truck and car stay in contact for 0.25 seconds. Calculate the car's acceleration and the truck's acceleration. Which one is bigger, and by what ratio? (Twice as much? Three times as much?)
    3. Let's say the truck has mass 1000 kg and the car has mass 500 kg. Assuming negligible friction with the road during the collision, the forces exerted by the car and truck on each other are the net forces experienced by each vehicle. Using the accelerations from part (b), calculate Ftruck on car and Fcar on truck.
    4. Your part (c) answers stem from your guess about how the car's change in velocity compares to the truck's change in velocity--a guess that reflects your "reaction" intuition. Does this intuition agree with Newton's 3rd law?
    5. We already knew that Newton's 3rd law is true. So what was the point of this whole question?
  4. In question 3, the intuition that the car reacts more than the truck during the collision leads to a conclusion ("the car's velocity changes twice as much as the truck's") that agrees with Newton's 3rd law. But in question 1, that same intuition leads many people to think that the truck exerts a larger force on the car than vice versa, a conclusion that disagrees with the 3rd law. What's going on here? How can the same intuition ("car reacts twice as much as truck") lead to two different conclusions, one of which is right and one of which is wrong?
  5. Here's how some people reconcile the paradox from question 4: "My intuition says that the car reacts more strongly than the truck reacts during the collision. But by thinking through my intuitions carefully in question 3, I found that my 'reaction' intuition is actually an intuition about _____________________, not force." Fill in the blank.