Question

Consider a helium balloon, attached by a string to the floor inside a car. If the car is speeding up, will the balloon be leaning forward or backward – or not be leaning at all? Explain your answer using Einstein's Principal of Equivalence.

Answer 1

Solution-

If the car is speeding up in forwarding direction (+ acceleration), the ballon will lean forward.

Einstein's Principle of Equivalence says "The gravitational field is just like an acceleration ",

When the car started to accelerate the air inside the car get pushed backward relative to the car. It creates the condition of pseudo on air inside the car as well as the balloon, but the balloon has less density than the air outside, the net force on the balloon will be towards forward.

Compare the driver and the balloon in this situation-

The driver will be pushed back when the car accelerates because the driver is constantly falling under the gravity and the inertial force wants to keep the driver at its initial place. As the concept of relative acceleration works(pseudo force). The effects of pseudo force are towards backward so the driver pushed back.

The balloon has an effective buoyancy force to push it upward, the effective pseudo force, in this case, is buoyancy so, the air pressure at the back of the car is more than what is at the front section(inside). The more pressure creates more thrust force. So, the net thrust of buoyancy will be forward that makes it lean forward.

The "Einstein's Principle of Equivalence" is valid because of the acceleration due to the force only matters for the force generated on the object, whether its gravity or its buoyancy.