Moving block on a moving incline

In summary, the conversation discusses a problem involving a moving block on an incline plane, with the complication of the incline itself being allowed to move on a frictionless surface. The speaker is seeking help in finding a solution and emphasizes the importance of working through the problem rather than simply receiving an answer. They also provide links to their personal website and a discussion forum for further reading.
  • #1
Living_Dog
100
0
I have thought and thought about this problem for years and made no progress.

First off, the moving block on an incline plane has a simple solution using Newton's laws for both friction and no friction cases. But once the incline plane itself is allowed to move, on a frictionless surface, then my problem begins.

Now what I am asking for is someone to help me work through the solution rather than just handing me an answer. This is not for any homework. I saw it years ago (Taylor? Goldstein??) and have never thought of posting it here until now.


Thanks!

-LD
________________________________________
my bread: http://www.joesbread.com/
my faith: http://www.angelfire.com/ny5/jbc33/
 
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  • #2
Let the incline have acceleration f, which for simplicity is parallel to the ground.

Now let the block have acceleration a relative to the incline. Note that this will be parallel to the slope of the incline.

However, the total acceleration of the block will be f+a. What this means is that the block will in fact accelerate into the plane of incline, so the component of its weight on the incline, minus the inclines reaction force will be nonzero. In other words, the reaction from the incline will not entirely cancel out the component of weight.

Note that the incline will have two forces on it. It's weight, and the reaction force from the block.

Now, draw a picture.
 
  • #3
Draw two separate FBD's.
 

Related to Moving block on a moving incline

1. How does the acceleration of a moving block on a moving incline compare to that of a stationary block on a moving incline?

The acceleration of a moving block on a moving incline is equal to the acceleration due to gravity times the sine of the incline angle. This is the same acceleration as a stationary block on a moving incline.

2. What factors affect the motion of a block on a moving incline?

The motion of a block on a moving incline is affected by the mass of the block, the incline angle, and the speed of the incline. Friction and air resistance can also affect the motion.

3. How can the motion of a block on a moving incline be described mathematically?

The motion of a block on a moving incline can be described using Newton's second law of motion, which states that the net force on an object is equal to its mass multiplied by its acceleration. This can be represented by the equation F=ma.

4. Can the motion of a block on a moving incline ever be completely frictionless?

No, it is not possible for the motion of a block on a moving incline to be completely frictionless. Even if the incline is perfectly smooth, there will always be some amount of friction present between the block and the incline, which will affect the motion of the block.

5. How does the angle of the incline affect the motion of a block on a moving incline?

The angle of the incline has a direct impact on the acceleration and speed of the block on a moving incline. A steeper incline will result in a greater acceleration and faster speed, while a shallower incline will result in a slower acceleration and lower speed.

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