Slipping off a Car Seat: What Determines Passenger Safety?

[Yam]

Homework Statement

A car traveling at 20 m/s stops in a distance of 60 m. Assume that the deceleration is constant. The coefficients of static and kinetic friction between a passenger and the seat are Us and Uk respectively. You may assume that the passenger is not in contact with anything else. Which of the following statements below is true?

a) The passenger will slip off the seat if he is light and remain on the seat if he is heavy.
b) The passenger will not slip off the seat regardless of the values of Us and Uk .
c) The passenger will slip off the seat regardless of the values of Us and Uk .
d) The passenger will not slip off the seat if Us> 0.4
e) The passenger will slip off the seat if Uk<0.3

Homework Equations

Kinematics : v^2 = u^2 +2as
Newton's second Law: F=ma
Force of Friction: Us*Normal Force

The Attempt at a Solution

a) The passenger will slip off the seat if he is light and remain on the seat if he is heavy.
The statement is too ambiguous.
b) The passenger will not slip off the seat regardless of the values of Us and Uk .
As long as F>UsN, the passenger will slip
c) The passenger will slip off the seat regardless of the values of Us and Uk .
As long as F>UsN, the passenger will slip
d) The passenger will not slip off the seat if Us> 0.4
e) The passenger will slip off the seat if Uk<0.3

I will attempt to find out the minimum Us that is required so that the passenger will not slip.

0 = 20^2 + (2)(a)(s)
a = 10/3
(m*g*Us)=ma
Us = 10/3g =0.34, which doesn't fit into any option above.

May i know if i made any errors in concept or calculation

 

[haruspex]

a) can be answered.
For all of them, you need to spot how to eliminate mass from the equation. Let the mass of the person be m. What is the normal force? What (given the speed and stopping distance) is the decelerating force needed?

 

[Yam]

0 = 20^2 + (2)(a)(s)
a = 10/3

frictional force = decelerating force
(m*g*Us)=ma <=== the mass is eliminated here from the equation
The normal force is mg, from the individual.

Us = 10/3g =0.34.

Is that right??

 

[haruspex]

0 = 20^2 + (2)(a)(s)
a = 10/3

frictional force = decelerating force
(m*g*Us)=ma <=== the mass is eliminated here from the equation
The normal force is mg, from the individual.

Us = 10/3g =0.34.

Is that right??

Sorry, I should have noticed you'd posted all that. I only looked at the answers you were proposing in red. For each question, you only need to answer true or false. Can you correct your answer to a)?
The 0.34 doesn't need to match anything exactly. What do you think the 0.34 represents?

 

[Yam]

I would say that 0.34 represents the minimum coefficient of static friction that the seat must have.

I see, so the best answer would be option A.

 

[SammyS]

0 = 20^2 + (2)(a)(s)
a = 10/3

frictional force = decelerating force
(m*g*Us)=ma <=== the mass is eliminated here from the equation
The normal force is mg, from the individual.

Us = 10/3g =0.34.

Is that right??

That's the correct acceleration, except for the sign, but that doesn't matter here.

The value for μ_S looks good.

That is covered by one of the choices.

 

[haruspex]

I would say that 0.34 represents the minimum coefficient of static friction that the seat must have.

The minimum such that she will not slide off, yes. So what would be the answers to d and e?
I see, so the best answer would be option A.

Option A? No, there are five questions and you must answer true or false to each.

 

[Yam]

a) The passenger will slip off the seat if he is light and remain on the seat if he is heavy.
False, a heavy passenger can still slip off with a low Us

b) The passenger will not slip off the seat regardless of the values of Us and Uk .
False, Us<0.34 will cause the passenger to slip

c) The passenger will slip off the seat regardless of the values of Us and Uk .
False, for the passenger to slip

d) The passenger will not slip off the seat if Us> 0.4
True, Calculated Us>0.34

e) The passenger will slip off the seat if Uk<0.3
Uk is not invloved.

Is this right?

 

[haruspex]

a) The passenger will slip off the seat if he is light and remain on the seat if he is heavy.
False, a heavy passenger can still slip off with a low Us

b) The passenger will not slip off the seat regardless of the values of Us and Uk .
False, Us<0.34 will cause the passenger to slip

c) The passenger will slip off the seat regardless of the values of Us and Uk .
False, for the passenger to slip

d) The passenger will not slip off the seat if Us> 0.4
True, Calculated Us>0.34

e) The passenger will slip off the seat if Uk<0.3
Uk is not invloved.

Is this right?

Pretty much, but your reason for (a) could be refined. As your equation tells you, the mass of the passenger has no relevance.

 

[Yam]

Oyes, i understand now, thank you for your help!