# Accelerating car and the person driving it

Hi

Can anybody explain why the top part of the body goes back when the car accelerates? Can you please explain in terms of newton's laws.

## Answers and Replies

russ_watters
Mentor
The top part of the body does not go back: the bottom part goes forward [faster] because it is attached to an accelerating car.

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Hi

Can anybody explain why the top part of the body goes back when the car accelerates? Can you please explain in terms of newton's laws.

Just to add a bit to Russ's (correct) answer.
Imagine watching the process from the ground outside the car (an inertial frame) in slow motion. You would see the car start to accelerate and move forwards. The bottom half of the body would do likewise, accelerated by forces from the car seat, which is (obviously) attached to the car. But there is a time-delay until a net force starts to act on the top half of the body (which we can think of as loosely coupled to the bottom half) and so it cannot immediately join in with the forward motion. From the ground it therefore stays still, but form the point of view of the driver (a non-inertial frame) it moves backwards.

Just to add a bit to Russ's (correct) answer.
Imagine watching the process from the ground outside the car (an inertial frame) in slow motion. You would see the car start to accelerate and move forwards. The bottom half of the body would do likewise, accelerated by forces from the car seat, which is (obviously) attached to the car. But there is a time-delay until a net force starts to act on the top half of the body (which we can think of as loosely coupled to the bottom half) and so it cannot immediately join in with the forward motion. From the ground it therefore stays still, but form the point of view of the driver (a non-inertial frame) it moves backwards.

Thanks for detailing it, infact this is exactly the way I wanted to understand. I keep feeling that I have started understanding about motion in accelerated frames, but I come across a scenario which I am not able to explain with the way I understand the laws.

Coming back to your explanation and particularly last sentence. Are you sure that viewed from ground (inertial frame) the head stays still but from non-inertial frame it moves backward?

Coming back to your explanation and particularly last sentence. Are you sure that viewed from ground (inertial frame) the head stays still but from non-inertial frame it moves backward?
That is my understanding. Perhaps one of the mentors could comment?

Thanks for detailing it, infact this is exactly the way I wanted to understand. I keep feeling that I have started understanding about motion in accelerated frames, but I come across a scenario which I am not able to explain with the way I understand the laws.

Coming back to your explanation and particularly last sentence. Are you sure that viewed from ground (inertial frame) the head stays still but from non-inertial frame it moves backward?

Imagine from the car's frame of reference: The driver is sitting normally, and then throws his head backwards to the seat.

From an inertial frame, the head wouldn't quite be still, as it's attached to the car through the body, but it would move much less than the accelerating car.

Thanks guys, i understood it now.

How would we explain following in similar way:

A accelerating train with a pendulum attached to its ceiling. Do we see the same angle it makes from non-inertial frame (train) and inertial frame (ground) and why?

rcgldr
Homework Helper
A accelerating train with a pendulum attached to its ceiling. Do we see the same angle it makes from non-inertial frame (train) and inertial frame (ground) and why?
The angle will appear the same regardless of the frame of observation (ignoring near light speed affects).

A accelerating train with a pendulum attached to it's ceiling. Do we see the same angle it makes from non-inertial frame (train) and inertial frame (ground) and why?

Because from the point of view of the outside, the train+attachment point is accelerating, but the pendulum is still, but from the train's point of view, the train+attachment point is still, but the pendulum is accelerating. However, both will agree that the acceleration is the same, but with opposite signs. (so the train is moving forward for outside perspective, but the pendulum is accelerating backwards for the train perspective.)

grettz...

The angle will appear the same regardless of the frame of observation (ignoring near light speed affects).

i think the acceleration will affect the way the pendulum swings. so i dont see how the angle remains unaffected. i m pretty bad at math, so cant work it out. but it doesnt seem right when i think about it.

i think the acceleration will affect the way the pendulum swings. so i dont see how the angle remains unaffected. i m pretty bad at math, so cant work it out. but it doesnt seem right when i think about it.

He didn't said the angle will remain unaffected due to acceleration, he said regardless the frame of observation. Different frames will see different accelerations,yes, because the train frame is a non-inertial frame, so it will have fiction forces on it force diagram. However, that fiction force is in magnitude equal to the force observed by a outside frame acting on the train.

Take some time to think about this, imagine and draw 2 force diagrams, one in the train, other outside, and verify for yourself. Don't forget whoever, that the train is non-inertia framel!? dv/dt≠0

(of course, like Jeff Reid right said, this is true assuming v<<c, not considering speed light effects)

grettz

yeah, my mistake. should have read jeff_reid's post more carefully.