Negative Acceleration Moving Forward
Location: South Africa
I have read a few books on a negatively
accelerating moving object. If the forward moving object is
accelerating negatively, many books claim that the dragging/
frictional force is greater than the forward thrust. If this
is true, then the net force acting on the object should point
backward and must sure cause the object to move backward but in
fact the object is slowing down but still move forward. Why?
If we just consider the forces acting on an object as either forward
or reverse having values of positive and negative, respectively, the
sum of the forces is the total force acting on the object. Therefore,
if a backward force is greater than the forward force, the net force
will be in the backward direction. Now, if an object is already
moving in the forward direction and a steady backward force is
applied, the object will begin to slow down, eventually stop and then
start moving backward at an ever-increasing speed. The acceleration
that the object experiences is directly related to how much force is
applied. Consider tossing a ball straight up into the air. As the
ball leaves your hand, the force exerted by gravity acts on the ball
and causes it to slow down. Eventually it stops at some point and
begins to fall back to the ground. Gravity is providing a downward
force that is acting on the moving object. Hope this helps!
A net force acting "backwards" on an object moving "forward" will
cause the object to slow down, but it can still move "forward".
Perhaps the best example is an airplane. During take-off, thrust
("forward force") is greater than drag ("backward force") and the
plane accelerates forward. This is a net forward force on the plane
and everyone in the plane feels it (and that is why you are seated
and seat-belted during take off).
When the plane reaches a "cruising state", all four forces (thrust,
drag, lift, and gravity) are balanced, so there is no net force on
the plane. The plane is still moving forward relative to the ground
(at around 400 to 500 mph usually, depending on the airplane and the
wind), but the net force is zero. People can get up and walk around
the cabin if the turbulence is not too bad.
When the pilot gets ready to land, he/she reduces the thrust from
the engines and the net force is "backwards" (negative) causing the
plane to slow down (but still move forward). This is an example
where the net force on the plane is negative, but the plane still
Usually, when the plane lands, the pilot also applies a reverse
thrust from the plane's engines to slow the plane down on the
runway. What would happen if the pilot did not stop applying this
reverse thrust? The plane would slow down to a stop, and then begin
to accelerate backwards (again, another example of a negative net
force being applied, to an object that moves forward, then stops,
then moves backwards). Although the plane's velocity would change
sign in this case (from positive (forward) to negative (backward)),
the net force and the net acceleration would be negative (backward)
during the entire time that the reverse thrust is being applied.
My physics students used to really struggle with this one. I would
talk about throwing a baseball up in the air. After the ball is
released from my hand, the only big force acting on the ball is
gravity (I am neglecting air resistance for the sake of
simplicity). So the net force on the baseball is always down
(toward the center of the Earth). Does that mean the baseball is
always MOVING down? No, it moves up about half the time (during
which the velocity is positive (upward) and decreasing) and down
about half the time (when the velocity is negative (downward) and
increasing -- until it hits the ground). So the ball can be moving
up (but slowing down) while a negative (downward/backward) net force
is applied to the ball. If it helps, remember F=ma. The force of
gravity is always acting on the ball (even when it changes direction
at the top of its trajectory), so "a" (acceleration) in F=ma can
never be zero.
I hope this helps!
An object will accelerate in the direction of the net force acting
on it. So if an object moves in a direction we call "forward," a
net force in the opposite direction ("backward") will cause it to
accelerate in the opposite direction (backward).
How can this be? How can an object be moving forward but
Simple. If it is moving forward and accelerating forward, that
means that it is speeding up. If it is moving forward but not
accelerating (its acceleration is zero) then its speed is
constant. If it is moving forward but accelerating backward, then
it is slowing down.
If the net backward force acts on the object for a long enough time,
the object will slow down, stop, and begin moving backwards, faster
and faster. You see this whenever an object is thrown into the
air. Its initial velocity is upward, but the net force on it
(mostly from gravity) is downward. So the object moves upward more
and more slowly, until at the top of its path it stops and begins
moving downward faster and faster.
Acceleration is NOT how an object is moving. Acceleration is how an
object's motion is CHANGING:
A real life example is a very heavy cart moving forward. You push backward
on the cart, providing a backward force on the cart. The cart does of
course push forward on you, but that forward force is on only you. The cart
feels the backward push and the backward acceleration. If you keep pushing
backward, if you do not fall down or give up, the cart slows to a stop and
then starts moving backward. If you keep pushing, the backward-moving cart
then speeds up.
Acceleration in the same direction as velocity speeds up an object.
Acceleration directed opposite of velocity slows down an object.
Acceleration on an object with zero velocity makes the object START to move
in the direction of the acceleration.
Dr. Ken Mellendorf
Illinois Central College
If you keep pushing backward, negatively, long enough, than sure,
the object will stop, and go the other way. But this has to be an
outside force. friction can make you stop ok, but it will not push
you back the other way, it depends on you moving in the first place
to even show up.
An easy example is throwing a ball up in the air. It is moving upward.
But it is getting a negative acceleration from gravity. It slows
its vertical climb, then stops, then turns around and comes back
down. The force has to work over a time to counter the inertia of
the object already moving upward. It will win, but not instantly,
it has to slow the rising ball. As a hint see that the upward
momentum, mass * velocity, has the same units as force * time.
kg * m/sec = kg m /sec/sec * sec
change in upward momentum = force * length of time force acts.
You start rising with a certain speed, and it takes time for the
gravity force to drop this to zero, then turn it negative.
Click here to return to the Physics Archives
Update: June 2012