# Friction??

• Dec 13th 2007, 06:43 PM
mrjohnson
Friction??
Heres a problem I cant get I've managed to solve equations like this without involving the equation for friction, but this is slightly more taxing, for me...

a ball of mass
m, position x(t) and velocity v(t) = dx/dt, where t is time. The equation of
motion of the ball is

m
dv/dt = μmg ,

where the only force on the ball is the friction,
μ > 0 is the constant coefficient of friction and g the acceleration
due to gravity.
Ball starts with initial speed
V0, at position x = 0 and t = 0.

(a)Solve equation of motion and determine
v(t).
(b)Solve d
x/dt = v(t), using the result from part (a), and determine x(t).
Find time
T at which ball stops.

If someone could get me started I'd appreciate it, what do I need to do to deal with the friction part?

dv/dt = -k/m*v => int dv/v = -k/mdt

v(t) = exp(-k/mt+C) = C'exp(-k/mt)

but this doesn't account for friction...

• Dec 13th 2007, 11:44 PM
Constatine11
Quote:

Originally Posted by mrjohnson
Heres a problem I cant get I've managed to solve equations like this without involving the equation for friction, but this is slightly more taxing, for me...

a ball of mass m, position x(t) and velocity v(t) = dx/dt, where t is time. The equation of
motion of the ball is

m
dv/dt = μmg ,

where the only force on the ball is the friction,

μ > 0 is the constant coefficient of friction and g the acceleration
due to gravity.
Ball starts with initial speed V0, at position x = 0 and t = 0.

(a)Solve equation of motion and determine v(t).
(b)Solve dx/dt = v(t), using the result from part (a), and determine x(t).
Find time T at which ball stops.

If someone could get me started I'd appreciate it, what do I need to do to deal with the friction part?

dv/dt = -k/m*v => int dv/v = -k/mdt

v(t) = exp(-k/mt+C) = C'exp(-k/mt)

but this doesn't account for friction...

It is already accounted for in the equation of motion:

$m \frac{dv}{dt}=-\mu m g$

This is the equation of motion of a body of mass $m$ moving on a horizontal
surface with no other force than friction (with the additional assumption that
the initial velocity is positive)

ZB

• Dec 14th 2007, 08:14 AM
topsquark
Quote:

Originally Posted by mrjohnson
m
dv/dt = μmg ,
where the only force on the ball is the friction,
μ > 0 is the constant coefficient of friction and g the acceleration
due to gravity.
Ball starts with initial speed
V0, at position x = 0 and t = 0.

(a)Solve equation of motion and determine
v(t).
(b)Solve d
x/dt = v(t), using the result from part (a), and determine x(t).
Find time
T at which ball stops.

dv/dt = -k/m*v => int dv/v = -k/mdt

Why are you using this equation of motion when one has already been given to you??

$m \frac{dv}{dt} = - \mu mg$

$\frac{dv}{dt} = - \mu g$

$v = \int (- \mu g) ~dt$

Just integrate.

-Dan