# What would be the truck's skidding distance?

## Homework Statement

use to answer 1 and 2. A truck driver slams on the brakes and skids to a stop through a displacement of x.
1.) if the truck's mass doubles, find the truck's skidding distance in terms of x.(hint:increasing the mass increases the normal force.)
a. x/4
b. x
c. 2x
d. 4x

2.) If the truck's initial velocity were halved, what would be the truck's skidding distance?
a. x/4
b. x
c. 2x
d. 4x

wudnt both of them be x/4 because if u increase the mass than the acceleration would decrease so the distance would decrease also and the only one less than x is x/4 and the same thing with initial velocity. if the ini. vel. is less than the acceleration would be less. but my teacher said that my answers were wrong. so please help.

## The Attempt at a Solution

For the first question, -Ff = ma. If Ff is proportional to the normal force, which is proportional to the mass in this case, does increasing the mass change the acceleration?

it should coz more mass would mean less acceleration by newtons second law and y would my reasoning be wrong for 2nd question? also doesnt Fnet=ma not Ff?

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But $$F_f=\mu mg$$ and $$-F_f=ma$$

doesnt Ff= umgcosX becuase Fn is mgcosX and than you have to find all the netforces to say is equal to ma

The normal force is equal but in an opposite direction to the gravitational force in this question. The only force acting in the direction of acceleration is the frictional force when a truck slams its breaks.

right?? so that means that more mass less acceleration

If $$-F_f=-\mu mg=ma$$ what happens if you increase the mass? How does it affect the acceleration?

the acceleration decreases.

Why would it decrease if the mass cancels out?

because lets say that the Ff was like 40N then changing the values of mass would decrease the acceleration.

if i may the acceleration you are talking about is the one that is stopping the truck. therefore logically and without all the equations the truck takes more time to stop and therefore more displacement.
your logic is right and u understood the question. friction always acts opposite to motion and so it stops the truck.
this acceleration is negative w.r.t. direction of motion....
now if you apply your equations it should give 4x

tmoan are you talking about the 1st or the 2nd problem because i thought it would be x/4 for both of them.

the first where the mass doubles

if i may the acceleration you are talking about is the one that is stopping the truck. therefore logically and without all the equations the truck takes more time to stop and therefore more displacement.
your logic is right and u understood the question. friction always acts opposite to motion and so it stops the truck.
this acceleration is negative w.r.t. direction of motion....
now if you apply your equations it should give 4x

But the friction depends on the normal force, wich depends on the mass of the truck.

A truck with 2x the mass will have 2x the normal force and thus 2x the friction force.
the acceleration will stay the same.

listen if there was no friction it slams intu a wall right in a millisecond. say the truck was moving at 20 km/h. in a millisec that became 0 km/ h. so it has a very large acceleration directed opposite of motion.
on the other hand take the friction case. friction doesn't stay the same because the sum of friction force during the whole stopping period will be constant from v =20 to v = 0.
but the difference is in acceleration.
you yourself said the acc decreases and you are right.

ur right the acceleration stay the same.
but since the friction force doubles.
ur right

but try to think of it this way if the truck was at a slow speed and you stood infront of it trying to stop it while walkin backwards with it. and u can only exert a constant force on the truck (ur the friction)
the truck will exert a force on ur hand.
if the truck had 2x mass it will exert more force on ur hand so you will take more time to stop such a force right=> more distance.
sorry i can't explain by simple equations.

lolzz i m soo lostt.. because more mass means less acceleration which means less displacement

hehe

lolzz ... lmao greatt ahhHH!!!!! i have no cluee wat i m doingg!!! i need a teacher who teaches instead of tellin us stories about his life and cracking lame jokes and that hehe was not cute!! lolz

you just proved me wrong and disproved yourself again.
m1 and m2
friction force
f1 = k N1 ;N1 = - m1g
f2 = k N2 ;N2 = - m2g = -2m1g
-kg is the acceleration of the friction at all times
ok

ya i get that in college.Alot

right.. do u teach?

nope i am a student 2nd year physics but my doctors are dumb. and those are PhD holders ...
bunch of crap