# Ramp Problem

#### Ninja_P

I would really appreciate some help on this problem, or even a push in the right direction:

An object of unknown mass slides down an incline in which &Theta;= 6.9. The object slides with a constant velocity of 1.4 m/s. At the bottom of the incline, the object slides on to a horizontal in which the coefficient of friction is the same as the incline. This is neglecting air resistance and the transfer of the object from incline to flat surface. I'm trying to figure out how long it will take the object to cease movement after it begins to slide on the horizontal surface.

So far I've been able to figure out:
Fnet = 0 since acceleration = 0.
Force of friction = Force parallel since Fnet = 0.
&mu; = 0.12101 because of tan&theta; = &mu;

Any help is greatly appreciated.

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#### Ninja_P

Of course, Fnet = ma
Normal Force = Weight x cos&Theta; On the horizontal -> W = mg
Parallel Force = Weight x sin&Theta;
Friction Force = &mu; x Weight x cos&Theta; (Normal Force)
and my four kinematics equations.

#### jamesrc

Gold Member
When you're on the horizontal part, the only force that is in the direction of motion is the friction force, which is now |f| = &mu;mg. Let's define the direction of motion as the positive direction, so:

Fnet = -&mu;mg
ma = -&mu;mg
a = -&mu;g

Now you have an acceleration that you can plug into your kinematic equations (vo is given as +1.4 m/s) to find the time to rest (v = vo+at is all you need for that).

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