Video Transcript
Which of the following statements
must be true? (A) If an even number of forces act
on an object, it must be accelerating. (B) If an even number of forces act
on an object, it must not be accelerating. (C) If an odd number of forces act
on an object, it must be accelerating. (D) If an odd number of forces act
on an object, it must not be accelerating. Or (E) none of these statements
must be true.
We’ve been asked whether an
object’s acceleration depends on the number of forces acting on it being even or
odd. To think about this, let’s recall
that an object will accelerate if there is a nonzero net force acting on it. Also remember that by net force we
mean the sum of all the individual forces acting on the object. Therefore, the net force simply
depends on the magnitudes and directions of all the individual forces. Whether there is an even or odd
number of individual forces does not necessarily determine anything about the net
force.
To illustrate this, we can think of
some examples that disprove each of the statements made in answer options (A)
through (D).
Option (A) says that if an even
number of forces act on an object, it must be accelerating. But imagine an object that has two
forces acting on it of equal magnitude and opposite direction. In this case, the object has zero
net force acting on it, so it is not accelerating. Therefore, answer option (A) is not
correct.
Option (B) says that if an even
number of forces act on an object, it must not be accelerating. But to disprove this, we can
imagine an object that has two forces acting on it of equal magnitude and
direction. In this case, the object has
nonzero net force acting on it and therefore is accelerating. So option (B) is incorrect as
well.
Next, (C) says that if an odd
number of forces act on an object, it must be accelerating. But we can see that in this example
diagram, an odd number of forces acting on an object can sum to zero, meaning the
object does not accelerate. So option (C) is not correct
either.
Moving on, option (D) says that if
an odd number of forces act on an object, it must not be accelerating. But it is entirely possible for an
odd number of forces to produce a nonzero net force, as shown in this example
diagram. So we know that (D) is incorrect as
well.
Thus, we know that option (E) is
the correct answer. We cannot make generalizations
about the net force or acceleration produced by an even or odd number of forces. So none of these statements must be
true.
