If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

### Course: Class 11 Physics (India)>Unit 9

Lesson 11: Treating systems

# Three box system problem

In this video David explains how to easily find the acceleration of a three box system by treating it as a single mass. Created by David SantoPietro.

## Want to join the conversation?

• Wait, isn't the friction force an internal force ?, i thought internal forces were not included in the easy way strategy.
• The table is applying the force of friction and the table is external to the system of the three boxes.
• The force of friction is shown to go to the left but does it not also go to the right?
It is being pulled from both sides.
• Friction opposes motion, thus it is to the left.
• What would happen if the total external forces on the system are negative due to friction?
• Nikolay's point on the reactive nature of friction to motion is right

but if your point of asking is about the situation in which a maximum friction happens to be large enough to offset the applied force (yes it is definitely possible and most non-moving bodies on a surface are doing exactly this), the answer is no motion at all as you may expect

for this specific case with the same masses of boxes, the smallest friction coefficient would be around 0.167 which makes the boxes not move. any bigger than this would require larger mass of the right box or smaller mass of the left one or the upper one on the table itself to make them move

hope this fill your curiosity a bit
(1 vote)
• How do we find out the direction of the acceleration of the whole system?
• The direction of acceleration(if there is an acceleration ) of the system is the direction of the larger mass hanging.
• since there are two strings shouldn't there be two different accelerations?
(1 vote)
• aren't the strings going to move together?
• Why do we have two different tensions?As we are using the same rope don't we have T on left side=T on right side.
• Two different ropes results in two different tensions. The tensions given by the weight of each mass hanging from each rope.
• Wouldn't the mass of the 12 kg object affect the acceleration of the system, and in turn, the force? Because, just like friction force, since the mass of the 2nd object is significantly larger than the other object, wouldn't it slow down or stop the acceleration and the force of the 5 kg object and basically the entire system?
• in fact, the reality is the opposite (friction could make the system faster)

1. if the friction is large enough to cancel out the net external force, the system simply don't move
2. if not, it lets them move as we saw in the example above
3. then, the friction applied to the system would change to friction of kinetic (sliding) than of static. and as we learned from previous videos, F_k <= F_s and in many cases you can say F_k < F_s. if that's the case of ours, the whole system would move faster toward left and downward than at the moment of starting to move

in short, friction plays a (kind of) role of a switch or a threshold. it turns on motion, if there's enough net external force applied. if not, it turns off and the system doesn't move. but once it starts to move, the friction could be smaller than when it began moving cause F_k <= F_s thus let the system move faster

one more thing, if your real concern is the effect of its sheer bigger mass of 12kg than 5kg of the right object, the friction itself is the effect. other than that? nope. that's why we need to only care the simple equation of Normal_force*Friction_coefficient to get an impact of this object and even the acceleration of the entire system
• Could we treat this example as a system even if there is no acceleration?
• Go on try it out yourself put a=0 in the equation and see what happens.
• Why is the horizontal frictional force counted as well? Is it because they are in a single system?