The net force on the system is the difference of the weights of the two masses (not the sum as is often reported).
You have to choose a positive direction of motion; there are two possible choices.
One of the choices is to choose the direction that makes the acceleration of the system positive. With this choice of direction:
The net force is 9.8 N and the acceleration is 9.8 N / (11 kg) = .9 m/s^2.
The 1.8 m/s^2 initial velocity is negative.
The system accelerates at .9 m/s^2 until the velocity is zero.
The motion interval is therefore characterized by v0 = -1.8 m/s, a = .9 m/s^2 and vf = 0.
Masses of 5 kg and 6 kg are suspended from opposite sides of a light frictionless pulley and are released.
Two forces thus act on the system, the 59 N force in the positive direction and the 49 N force in the opposite direction, giving us a net force of about
F_net = 59 N - 49 N = 10 N.
The mass of the system is 11 kg. A net force of 10 N on a system of mass 11 kg results in acceleration
a = F_net / m = 10 N / (11 kg) = .9 m/s^2, approximately.
If you give the system a push so that at the instant of release the 5 kg object is descending at 1.8 meters / second, what will be the speed and direction of motion of the 5 kg mass 1 second later?
If the 5 kg mass is descending at 1.8 m/s, then the velocity of the system is -1.8 m/s (note that all directional quantities must be referenced to our original choice of positive direction).
An acceleration of .9 m/s^2 means that in 1 second the velocity of the system will change by `dv = a `dt = .9 m/s^2 * 1 s = .9 m/s. This will give us a velocity of vf = v0 + `dv = -1.8 m/s + .9 m/s = -.9 m/s. That is, the 5 kg object will still be descending, but at .9 m/s rather than at 1.8 m/s.
During the first second, are the velocity and acceleration of the system in the same direction or in opposite directions, and does the system slow down or speed up?
During this 1-second interval the acceleration is positive and the velocity remains negative. So velocity and acceleration are in opposite directions. Whenever this is the case the object is slowing down, as it clearly is in this example.
If another second passes then the object's velocity will be near zero. After reaching the state of rest for an instant, the continuing acceleration will result in a positive velocity (6 kg mass descending), which with the positive acceleration will then begin speeding the system up.
Common errors:
It is very common for students to add the two masses and multiply by the acceleration of gravity, and present this as the net force on the system. This is not an unreasonable thing to do, but it
Possible misconceptions about direction:
STUDENT ANSWER: Since the acceleration is positive and the velocity of
the 5 kg object is negative, they are moving in opposite direction, and the
system is therefore slowing down.
<h3>Good, but you might (or might not) have a few misconceptions. Consider the
following:
It isn't a necessary to refer to the motion of the 5 kg object as being negative, nor is it a good idea to refer to the motion of the two masses as being in opposite directions. When you analyze the system, the motion of the system is positive or negative at any given instant; considered as part of the system, the individual parts don't have different directions of motion.
You haven't chosen a positive direction for the 5 kg object; you've chosen a
positive direction for the system. So it's not appropriate to refer to the 5 kg
object as moving in the negative direction. You could choose a positive
direction for the 5 kg object, but that choice would be completely independent
of the positive direction you choose for the system.
You chose the positive direction of the system as the direction opposite to that
in which the 5 kg object descends. Thus your chosen positive direction is the
direction in which the system is moving when 6 kg object descends.
Acceleration and velocity are two different quantities. The acceleration of this
system has nothing to do with the direction in which one object or another is
moving. The acceleration is .89 m/s^2, according to your choice of the positive
direction of the system, and it doesn't matter if the system is moving in the
positive or the negative direction.
Your chosen positive direction for the system therefore entails ascent of the 5
kg object and descent of the 6 kg object.
The system has only one direction of motion at any instant; it can't be moving
upward and downward at the same time. For your choice of positive direction:
If the 5 kg object is ascending then the 6 kg object is descending, then the
system is moving in its positive direction.
If the 5 kg object is descending then the 6 kg object is ascending, then the
system is moving in its negative direction.
For your choice of positive direction, the acceleration of the system is +.89
m/s^2, and the initial velocity is -1.8 m/s^2, so after 1 second the system is
moving at -.91 m/s. This means that the 5 kg object is still descending and the
6 kg object is still ascending; but the entire system is moving in the negative
direction.</h3>
QUESTION ABOUT HOW THE LESSER MASS COULD BE ASCENDING:
I don’t understand how the 5kg object can be descending, shouldn’t it be
ascending?
INSTRUCTOR RESPONSE:
Not if the system was given a push to start it in the opposite direction.
If you throw a ball up into the air its acceleration is down but its initial
velocity is up. That situation eventually brings it to rest, after which it
starts moving (and speeding up) in the downward direction.
Very similar situation here.