Sliding Block Problem: Finding Distance Traveled

[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.

 

[Astronuc]

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 v_o² = 2 a x, where v_o is the initial velocity, a is the acceleration (or deceleration) determined from the forces of gravity and friction, and x is the distance traveled.

 

[Pseudo Statistic]

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.

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

 

[Hootenanny]

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

 

[ksle82]

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 v_o² = 2 a x, where v_o is the initial velocity, a is the acceleration (or deceleration) determined from the forces of gravity and friction, and x is the distance traveled.

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, v_o is the initial velocity. How did you arrive at v_o²=2ax astronuc?

 

[Astronuc]

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, v_o is the initial velocity. How did you arrive at v_o² = 2ax astronuc?

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 = v_o, and the final velocity v₁ = 0. Multiply the equation by 2 and divide by m and one obtains,

v_o² = 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 v_o 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