# Newtons Laws on a sliding box

## Homework Statement

A box is given a push so that it slides across the floor. How far will it go, given that the coefficient of kinetic friction is 0.18 and the push imparts an initial speed of 4.1 m/s?

## Homework Equations

MG of the object = mass * 9.8
Friction = mg * 0.18

## The Attempt at a Solution

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ANY HELP WOULD BE MUCH APPRECIATED

tiny-tim
Homework Helper
Hi tigerwoods99!

Use the work-energy theorem …

work done = change in energy

sorry, im not familiar with this theorem

tiny-tim
Homework Helper
sorry, im not familiar with this theorem

oops!

In that case, find the acceleration from µ = 0.18, and then use one of the standard constant acceleration equations, with vi = 4.1 and vf = 0.

That would make sense. I know the acceleration has to be negative because it comes to a stop, the acceleration is -> (direction) and the friction is <- (direction)

Are these the formulas I could use to find the acceleration using mu? I have a feeling i have to know the weight of the object though to find the mg and fn
a = Fnet/m
Ffriction = Fnormal * mu

Vi: 4.1 m/s
Vf: 0 m/s
D:
A:
T:

ideasrule
Homework Helper
If a=Fnet/m, Fnet=Fnormal*mu, and Fnormal=mg, then a=?

yes, i understand the formulas but how do i get the values for the different forces, if the mass of the object is unknown?

ideasrule
Homework Helper
Just assume the mass is m and try it. You'll find that m cancels out.

A = Fnet/m
A = (Fnormal *mu)/m

A = (Fnormal *u) ?
So how would I find the FN

ideasrule
Homework Helper
Fn exactly balances gravity, or else the object would accelerate in the y direction. So Fn=mg.

BTW:

A = (Fnormal *mu)/m
A = (Fnormal *u) ?

mu = mg/9.8 * u

ideasrule
Homework Helper
"mu" is a single constant, representing the coefficient of friction. It is not m*u, so mu/m isn't equal to u (which is meaningless).

thats what i thought, but wasn't sure becuase i am used to seeing it as just u

a = fnet/m
a = (fnormal * mu)/ m
a = (mg * mu)/m
a = gravity * mu

but becuase the object is moving vertically there is no acceleration

ideasrule
Homework Helper
Yes, that's right

tiny-tim
Homework Helper
Hi tigerwoods99!

(just got up :zzz: …)
A = Fnet/m
A = (Fnormal *mu)/m

A = (Fnormal *u) ?
So how would I find the FN
mu = mg/9.8 * u
thats what i thought, but wasn't sure becuase i am used to seeing it as just u

(oh, if only everybody had a Mac instead of a PC, with a sensible keyboard! )

have a mu … µ
a = fnet/m
a = (fnormal * mu)/ m
a = (mg * mu)/m
a = gravity * mu

but becuase the object is moving vertically there is no acceleration

(try using the X2 tag just above the Reply box )

Are you confusing the vertical and horizontal accelerations?

Vertically, a = 0, and Fnet = N - mg, so N = mg.

Horizontally, Fnet = µmg, so ma = µmg.

thanks i got it!