Why is it when you suddenly stop a car people and packages fly forward a helium balloon inside the car goes backwards?

There will, however, be a second effect. Because the air in the car tends to stay in motion, it will move forward as well. It will be compressed at the front of the car and made less dense at the back. This means the air nearer the front of the car will be at higher pressure than the air at the back. Looking at the small bit of air around the balloon, this means there will be more pressure on the front of the balloon than the back. This imbalance of pressure means there is a backwards force on the balloon.

Both of these effects are present on the people, the packages and the balloon. The imbalance in air pressure is pushing the people and packages backwards as well. It is just that people are quite dense (have a lot of mass per cubic inch), whilst helium balloons have a lower density. (Have very little mass per cubic inch.) This means the first effect will be much bigger than the second for people and packages. The second effect will, in fact, be negligible for those folks and the goods they're transporting. They'll all tend to keep moving forward. But the second effect will be a bit bigger than the first for a helium balloon. The net result is that people and packages will continue in motion forward whilst the balloon is "pushed backwards."

In fact we can predict which objects will go forwards and which will go backwards. It depends on whether or not they have a higher density than air or to put it another way on whether they are lighter than air. When a car is braking, anything goes forward in the car (owing to inertia). Objects with a density greater than air are affected more by their momentum than the differential air pressure set up in the vehicle when it brakes. But with the helium balloon, it's different. Helium is one of the few gases which is lighter than air (less dense than air), so it always floats in the air, and it will "float" backward in this instance.

Gravity or acceleration?

In fact, it is a general principle that gravity and acceleration are indistinguishable. Suppose you have some tabletop physics experiment which you can perform in a room at home. Now suppose you take the entire room and put it inside a rocket, with the floor towards the back of the rocket. Suppose you put the rocket in deep space and turn the engines on, so that it accelerates forwards at 9.8 m/sec/sec (the acceleration due to gravity on the earth's surface). The result of the experiment will be exactly the same as it was at home.
Similarly, if you ever find yourself in an elevator in freefall (with no chains, friction or air resistance), you will feel exactly as if there was no gravity at all. This is because the downward acceleration of the lift is equivalent to a gravitational field pulling upwards, which exactly cancels the force of gravity pulling down. Astronauts use this principle when training for zero gravity.
In this example, the deceleration of the car can be viewed as an extra gravitational force pushing forwards. This simplifies things: you can pretend that the car isn't moving, and that it's in a gravitational field slightly stronger than normal, with gravity pulling diagonally downwards. From this point of view, the passengers fall "down" (forwards), while the helium balloon floats "upwards" (towards the back of the car).

First answer by Tigr. Last edit by Pure.mathmo. Contributor trust: 71 [recommend contributor]. Question popularity: 73 [recommend question]