Determining an expression for acceleration

In summary, the problem involves three blocks on top of each other, with the assumption that they are not moving. Using the equations F=ma, N=mg, and friction=umg, the free-body diagrams for each block are drawn. The equations of motion need to be written, including a geometric equation that ensures block 2 stays on block 1.
  • #1
kobylorat
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Homework Statement



Here is the question: http://i1110.photobucket.com/albums/h459/granolup/Untitled.png

It is assumed that the blocks are not moving.

Homework Equations



F=ma
N=mg
friction = umg

The Attempt at a Solution



I have started out drawing free-body diagrams for each of the three wedges.
For m1, there is a force due to gravity pointing downwards, a normal force pointing to the top right.
For m2, there is a force due to gravity pointing downwards, a normal force pointing to the bottom left, and the force of kinetic friction pointing to the top left.
For m3, there is a force due to gravity pointing downards, and a normal force pointing upwards.
 
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  • #2
welcome to pf!

hi kobylorat! welcome to pf! :wink:
kobylorat said:
I have started out drawing free-body diagrams for each of the three wedges.
For m1, there is a force due to gravity pointing downwards, a normal force pointing to the top right.
For m2, there is a force due to gravity pointing downwards, a normal force pointing to the bottom left, and the force of kinetic friction pointing to the top left.
For m3, there is a force due to gravity pointing downards, and a normal force pointing upwards.

ok so far (but isn't there also a friction force from the ground, and between 2 and 3?) …

now write out the equations of motion, including a purely geometric equation which specifies that block 2 stays on block 1 :smile:
 

Related to Determining an expression for acceleration

1. What is acceleration and how is it different from velocity?

Acceleration is the rate at which an object's velocity changes over time. It is different from velocity because velocity only refers to an object's speed and direction, while acceleration also takes into account how quickly the speed or direction is changing.

2. How is acceleration calculated?

Acceleration can be calculated by dividing the change in velocity by the change in time. The equation for acceleration is a = (vf - vi)/t, where vf is the final velocity, vi is the initial velocity, and t is the time interval.

3. Can acceleration be negative?

Yes, acceleration can be negative. This means that the object is slowing down or changing direction in a negative direction. For example, if a car is moving east and then starts moving west, its acceleration would be negative.

4. What is the difference between average and instantaneous acceleration?

Average acceleration refers to the overall change in velocity over a certain time period, while instantaneous acceleration refers to the acceleration at a specific moment in time. Average acceleration can be calculated using the change in velocity over a longer time period, while instantaneous acceleration would require taking the derivative of the velocity function at a specific time.

5. How can acceleration be determined from a position vs. time graph?

Acceleration can be determined from a position vs. time graph by finding the slope of the curve at a specific point. The slope of the curve represents the object's velocity at that point, and the change in slope over time represents the object's acceleration.

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