# Sliding Block Problem

1. May 23, 2006

### ksle82

https://www.physicsforums.com/attachment.php?attachmentid=6991&stc=1&d=1148442038
rocket1.JPG
Given the data in the drawing, find the total distance the sled travel.
I got stuck after summing all the forces in the X direction. Help! Here's what i have so far.

Sum of all Forces in X Dir: mgsin(theta) - f = ma
where mgsin(theta) is force due to gravity in the x-dir,
and f is the friction force.

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2. May 26, 2006

### Astronuc

Staff Emeritus
There is insufficient information to solve the problem.

The sled presumably has an initial velocity (not given), and there is a component of gravity acting in the -x direction and friction, which also acts in -x direction.

Since the final velocity is zero, one can use vo2 = 2 a x, where vo is the initial velocity, a is the acceleration (or deceleration) determined from the forces of gravity and friction, and x is the distance traveled.

3. May 26, 2006

### Pseudo Statistic

Why are you assuming the gravitational force and frictional force are in opposite directions? They should both be down the incline.

4. May 26, 2006

### Hootenanny

Staff Emeritus
Is this incline infinitly long or does it leave the incline at some point and become a projectile? Eitherway there is not enough information. I am assuming that the u is the co-efficent of kinetic friction.

~H

5. May 26, 2006

### ksle82

Yes i do feel that's the question is rather vague or doen'st have enough info. But i just copied out of the study package that was given to me.

Yes, vo is the initial velocity. How did you arrive at vo2=2ax astronuc?

6. May 26, 2006

### Astronuc

Staff Emeritus
That's actually a special case for constant acceleration.

The change in kinetic energy is equal to the product of the force applied over a distance, or

1/2 m v22 - 1/2 m v12 = m a x. Let v2 = vo, and the final velocity v1 = 0. Multiply the equation by 2 and divide by m and one obtains,

vo2 = 2ax

For the problem stated, the x component of the gravitation force is constant (it doesn't change over a short distance) and one assumes that friction is contant. The force due to friction is proportional to the normal force of the sled on the surface of the slope.

If vo is sufficiently large, then the distance traveled could be significant and the acceleration due to gravity would vary as a function of the altitude (height).

One may find this useful - http://hyperphysics.phy-astr.gsu.edu/hbase/mot.html#mot1