Competency #1

Answer and Explanation

The correct answer is B.

Lets analyze our choices to see why this is correct.

  1. The hammer and the feather must have the same weight.

    For this to be true, the hammer and the feather must have the same mass. Think about them on earth, a hammer is much heavier (has more mass so it has more weight) than a feather. Taking them to the moon does not change the amount of mass in the objects, so the hammer must still weigh more than the feather (although both weights will decrease as compared to the weight on earth). This statement cannot be correct.
  2. The hammer and the feather must undergo the same acceleration.

    Acceleration has to do with how fast an objects velocity is changing (how much an object speeds up or slows down). Since both objects start at rest, and wind up traveling the same amount of distance in the same amount of time, they both must have experienced the same rate of acceleration. This one must be true. If it was not, you would have observed one object hitting the ground before the other.
  3. The hammer and the feather must have the same net force acting on them

    This is a very common explanation, but is incorrect! Lets look at the Newton's second law:

Acceleration = Fnet / mass

We know from answer B, that both object experience the same acceleration. At the same time, we also know that the hammer has a greater mass than the feather (answer A). Since the hammer has a larger mass, it must have a larger force acting on it to get the same acceleration. For example, what net force would be required for each object to have an acceleration of 2 m/s2 if the mass of the feather was 1 kg and the mass of the hammer was 5 kg?

Hammer Feather
Acceleration 2 m/s2 2 m/s2
mass 5 kg 1 kg
Fnet ? ?
Acceleration = Fnet / mass 2 m/s2 = Fnet / 5 kg 2 m/s2 = Fnet / 1 kg
Fnet = 10 N Fnet = 2 N

Another way of looking at this answer is to draw a force diagram for the two objects. Very quickly, you see that the only force acting on the objects is the Fg. We know that the Fg for hammer is greater, and since only one force is acting on the object Fnet= Fg. Therefore, the Fnet for the hammer must be greater.

D. More than one of these must be true. This is false. Only statement B is true.

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