# Free fall and contact force

If two bodies are stacked on on top of other and in free fall and there is no contact force how come they remain in contact ignoring drag.

Secondly if two object were at rest say on table and table is removed so they are in free fall, first there was normal reaction between the two objects. Now in free fall the normal reaction disappears, if it disappear then what happen to distance between the two objects and what happens after the instant the contact force disappears. Will they remain stacked or not.

1. They remain in contact in free fall because they are both accelerating by exactly the same amount, since their acceleration is $$g$$, and independent of mass. (This is, of course, because you're ignoring drag and other such forces. Therefore, the only external force acting on the objects is gravity.)

2. The instant the reaction force from the table disappears, the objects are in free fall. As a result of the previous point (if you ignore drag etc.) the two objects will seem to fall as if they continue to be stacked one on top of the other.

• How can there be no contact force between two bodies stack one top of another during free if they are in contact May 17, 2021 at 9:30
• I'm not sure I understand, so correct me if I've got your question wrong. Contact does not imply force. Take a different example: consider two identical boxes sitting side-by-side on a table, touching each other. Both the boxes experience a reaction force from the table, but despite the fact that they are touching, they are not exerting a force on each other. May 17, 2021 at 9:35
• If you want another example more similar to your problem, consider this: you're on an elevator and you're standing on a weighing balance. The elevator is at rest with respect to the building, and so it reads your weight say, 80 kg (you lucky devil). Now, imagine the elevator starts to move downwards with some acceleration $a$: the net acceleration that both you and the weighing machine feel is now less than $g$: in fact, it is exactly $g-a$. This is because the net force the floor is exerting on the weighing balance has reduced. (contd.) May 17, 2021 at 9:41
• So can two bodies be in contact have no contact force May 17, 2021 at 9:42
• (contd.) As the elevator starts to accelerate faster and faster, the force that the weighing balance will read will go closer and closer to $0$, until -- at $a = g$ -- the net force that you exert on the weighing balance will go to zero. In this "weightless" state, your feet are "touching" the balance, but not exerting a force due to gravity on it. Of course there may be other forces like surface tension, or electrostatic forces and so on. If you want to take those into consideration, the problem will change (I assumed there to be no such forces). What "contact forces" are you considering? May 17, 2021 at 9:44

If the two bodies have the same mass I guess it makes sense that they remain in contact. If they don't, then Newton's second law tells us that they both receive the same acceleration anyways (the mass cancels out with the gravitational force). So then if you ignore drag force, with the same initial conditions they will remain in contact.

As there are no resistive forces in this scenario then its conclusive that they are being pulled down by earth by an amount of force which is equal to the magnitude of their weight and it's quite evident that it's the only force which is acting on them. Interesting part here is that they have same acceleration which is nothing but $$g=9.8m/s²$$ and they have same initial speed,here in this specific case it's $$0$$. So the amount of distance say block $$1$$ will cover downwards in time $$t$$ is $$\frac{gt²}{2}$$ and it will be same as the distance covered by say block $$2$$ in time $$t$$. This is the sole reason that they remain in contact throughout free fall.

When we are talking about contact forces here, we have to think about Normal reaction and friction.

Normal reaction is applied by a rigid surface on a body to prevent it's motion into the surface. Normal reaction should always be seen after the net force on the body has been calculated.

Friction comes in place when there is relative slipping of a point on a rough surface.

1. Here both bodies are moving with the same acceleration due to gravity. There will be no normal reaction since the bodies are moving with same acceleration and velocity at a point and are not colliding hence they will not fly off. If the objects are considered smooth there is no friction either. If the objects were considered rough and they had some torque, then might have been friction which would have not let the bodies to stay in contact.

2. When the bodies were on the table, the body stacked on the top of the other had a force due to weight, this force was balanced by the normal reaction from the body underneath. Now when the table is removed, then again it acts like case 1. The bodies start with same initial velocity and have same acceleration due to gravity, hence they always have same velocity at a particular time frame and are not colliding or not trying to attain the same position as the other object. Hence there is no normal reaction to set them apart, so they will continue to be at a state of free fall while staying in contact.