course Phy 231
OK, after receiving some helping in solving this problem:When two opposing masses are suspended on opposite sides of a pulley, both masses do not accelerate at 9.8 m/s^2.
Rather, the masses will accelerate in opposite directions. Therefore, when given two masses, 5 kg and 6 kg, that are suspended from a light, frictionless pulley, we can determine the net force of the system and magnitude and direction of the acceleration.
Setting the 6 kg mass side as the positive direction, and the 5 kg mass side as the negative direction, the weights are calculated as follows:
6 kg * 9.8 m/s^2 = 58.8 N
5 kg * 9.8 m/s^2 = 49 N
58.8 N - 49 N = 9.8 N
Since we know the mass of the system is about 11 kg (5 kg + 6 kg), we can determine the acceleration of the system as F = m * a, or a = F / m
a = F / m
a = 9.8 N / 11 kg = 0.89 m/s^2
If the system is given a push such that the 5 kg object (negative direction) is descending at 1.8 m/s, what will be the motion of the 5 kg object 1 s later:
v0 = -1.8 m/s
a = 0.89 m/s^2
'dt = 1 s
a = 'dv/'dt, or 'dv = a * 'dt = 0.89 m/s^2 * 1 s
'dv = 0.89 m/s, therefore:
'dv = vf - v0
0.89 m/s = vf - (-1.8 m/s)
vf = 0.89 m/s - 1.8 m/s = -0.91 m/s
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.
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.