# Newton's first law problem

## Homework Statement

Susan is standing in an empty Metro (subway) car which is travelling at constant velocity. Suddenly, because of an emergency, the driver applies the brakes. Select True or False for each of the following statements.

a) If she immediately grabs onto the seat behind her (she is facing forwards), then she must push on the seat to avoid falling.
b) If she immediately jumps straight up into the air, she will land closer to the front of the car.
c) She falls forwards -- i.e. towards the front of the car.
d) She falls because there is no force acting on her which can be large enough to slow her down.

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## The Attempt at a Solution

I'm stuck on this exercise. I think that statement a), b) and c) should be true because as when the train breaks, the train moves while the girl isn't, and this would imply that the girl gets thrown forward. However, I'm not sure on the wording of statement d). I'm also in doubt with statement a), as if she pushed on the seat she would simply go forward.

## Answers and Replies

tiny-tim
Homework Helper
hi fogvajarash!

hint: if there were no friction, at what speed would she move?

at what speed does the train move?

what does the friction actually do?

hi fogvajarash!

hint: if there were no friction, at what speed would she move?

at what speed does the train move?

what does the friction actually do?
If there were no friction, she would move forward as the train moves backward. and the train should move at a constant velocity until the train brakes and its speed decreases. Shouldn't the friction cancel out the force that causes the negative acceleration?

tiny-tim
Homework Helper
hi fogvajarash!

(just got up :zzz:)

if there were no friction, she would move forward at the same speed while the train would move forward more slowly

never mind how strong the friction is, where does it act? (and what does it do)?

hi fogvajarash!

(just got up :zzz:)

if there were no friction, she would move forward at the same speed while the train would move forward more slowly

never mind how strong the friction is, where does it act? (and what does it do)?
The friction acts in the direction that is opposite to the motion of the train. Then, i'm guessing that the girl should be thrown forward as there are two forces that reduce the train's acceleration, but the girl stays moving? (i'm assuming you are referring to the friction of the train) If it's the friction of the trains' ground, then her speed would be reduced and she wouldn't be pushed so hard?

Thank you very much for coping with me!

tiny-tim
Homework Helper
hi fogvajarash!

i'm sorry to be fussy, but you haven't answered my questions …

where does the friction act (on the girl)?

and what does it do? (not why, only what)​

hi fogvajarash!

i'm sorry to be fussy, but you haven't answered my questions …

where does the friction act (on the girl)?

and what does it do? (not why, only what)​
It acts.. By reducing her speed when she moves forward?

tiny-tim
Homework Helper
where does it act?

where does it act?
I don't get the problem or the question, I'm sorry. It should act on the ground?

I've done some real testing today and i've realized that when the train brakes, you get pushed forward.

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I think that the answer should be b and c. The girl is still moving at constant velocity while the train suffers from a negative acceleration (so she should go forward).

tiny-tim
Homework Helper
hi fogvajarash!

(just got up :zzz:)
I don't get the problem or the question, I'm sorry. It should act on the ground?

you have to think of these problems in terms of forces on the body in question (in this case, Susan)

a force has a magnitude, a direction, and a line (or point) of application

you have to specify the point of application (or mark it on your diagram)

there are only two forces on her, her weight (which acts through her centre of mass), and the friction from the floor (which acts on her feet)

what effect does the friction have? obviously, it makes her feet stick to the floor … in terms of speed, it makes her feet have the same speed as the train!

(and the magnitude doesn't really matter)

carry on from there

So, in the case to contrast the situation that happens when in a car that brakes suddenly, in a car you get thrown forward because you are seated, and this means that no other force is acting on you (there's no friction). Then that's the reason why you get thrown forward (as there is no force acting on you and you continue at constant velocity and the car just brakes).

So applied to this case it would happen that when she is seated, she must push on the seat and when she jumps, she would get thrown forward as there is no point of contact between the force and her. Then, when she is on the train ground, she will get affected by the friction and thus not get thrown forward. So this would mean that option c and d are incorrect? (However, when i was in the metro, why was i thrown forward (or so it seemed) when i was standing on the metro's ground?)

tiny-tim
Homework Helper
So, in the case to contrast the situation that happens when in a car that brakes suddenly, in a car you get thrown forward because you are seated, and this means that no other force is acting on you (there's no friction).

there's plenty of friction

from a seat, there's almost as much friction as from a floor

the only time you need a seat belt (or an airbag) in a car is when the car crashes (because then the friction is large, but not enough to stop you)
Then, when she is on the train ground, she will get affected by the friction and thus not get thrown forward.

that isn't physics

describe the forces

use the laws of resultant forces and moments

Thank you tim, i finally understood the problem. The girl moves forward in the train as she continues at constant velocity.

tiny-tim
Homework Helper
Thank you tim, i finally understood the problem. The girl moves forward in the train as she continues at constant velocity.

no, she doe not move forward at constant velocity

there is an external horizontal force on her (the friction from the floor on her feet)

no, she doe not move forward at constant velocity

there is an external horizontal force on her (the friction from the floor on her feet)
I just talked to my professor and apparently (he didn't state the fact) we aren't considering friction in this situation. So then would she continue at constant velocity? (only if there's friction she wouldn't move at constant velocity then?)

tiny-tim
Homework Helper
I just talked to my professor and apparently (he didn't state the fact) we aren't considering friction in this situation. So then would she continue at constant velocity?

ahhhh!

in that case, yes , she continues to move at the same speed that the train had before it braked

(though i don't see how that can be called "falling" as in the question )
(only if there's friction she wouldn't move at constant velocity then?)

if the friction is enough to keep her feet fixed to the floor, then she will fall, rotating forwards

if the friction isn't enough, then she will begin by rotating forwards, with her feet fixed, but after a short time her feet start to slide, and therefore she won't fall as fast as in the first case