Position of Block on Incline w/ & w/o Friction

In summary, the position of the block as a function of time for both cases (a) friction and (b) frictionless is represented by the equations: a) x(t)= .5g(cos(theta)-sin(theta))t^2 and b) x(t)= .5gsin(theta)t^2. The coefficient of friction is not given, but can be calculated using the relationship between the coefficient of static friction and the angle at which the object just begins to slide. The x-axis is along the incline in both cases.
  • #1
ksle82
30
0
Find the position of the block as a function of time for both cases:
a)friction
b)frictionless

Here're my answers. Please check to see if they're correct. The free body diagram are attached.

https://www.physicsforums.com/attachment.php?attachmentid=7068&stc=1&d=1149476915
slidingblock.JPG

a) x(t)= .5g(cos(theta)-sin(theta))t^2
b) x(t)= .5gsin(theta)t^2
 

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  • #2
Although I can't see your attachments , where's the coefficient of kinetic friction in the first part of the question ?
Also is your X-axis along the incline ?
 
  • #3
arunbg said:
Although I can't see your attachments , where's the coefficient of kinetic friction in the first part of the question ?
Also is your X-axis along the incline ?

coefficient of friction is not given, so i just assume it's mu (u). i don't know if one can do this or not. But if one has to calculate it, u is usually tan(theta).


And yes, x-axis is along the incline.
 
  • #4
ksle82 said:
coefficient of friction is not given, so i just assume it's mu (u). i don't know if one can do this or not. But if one has to calculate it, u is usually tan(theta).
That's not true, in general. What you are probably thinking of is the relationship between the coefficient of static friction (between an object and a surface) and the (special) angle at which the object just begins to slide. For that specific angle, [itex]\mu_s = \tan\theta[/itex].

But what you what is the coefficient of kinetic (sliding) friction, assuming the object starts from almost rest. What's the exact statement of the problem?

Your free body diagram looks OK to me.
 

1. What is the position of a block on an incline with friction?

The position of a block on an incline with friction is dependent on the force of gravity pulling the block down the incline and the opposing force of friction pushing back against the block. This creates a net force that causes the block to move down the incline at a slower rate than it would without friction. The exact position of the block can be calculated using the equations of motion and taking into account the coefficient of friction between the block and the incline surface.

2. How does the coefficient of friction affect the position of the block on an incline?

The coefficient of friction is a measure of the resistance between two surfaces when they are in contact. In the case of a block on an incline, the coefficient of friction between the block and the incline surface affects the position of the block by creating an opposing force that slows down the block's movement. A higher coefficient of friction means a greater resistance and a lower coefficient of friction means a lower resistance, resulting in the block being at a different position on the incline.

3. What is the position of a block on an incline without friction?

The position of a block on an incline without friction is dependent solely on the force of gravity pulling the block down the incline. This means that the block will accelerate down the incline at a constant rate and its position can be calculated using the equations of motion. Without friction, the block will continue to slide down the incline until it reaches the bottom or until another force acts upon it.

4. How does the mass of the block affect its position on an incline with and without friction?

The mass of the block does not directly affect its position on an incline with and without friction. However, the weight of the block, which is proportional to its mass, does affect the force of gravity pulling the block down the incline. This means that a heavier block will have a greater force of gravity pulling it down the incline, resulting in a different position compared to a lighter block. Additionally, a heavier block will have a greater normal force pushing against the incline, which can affect the force of friction and therefore the position of the block.

5. Can the position of a block on an incline change over time?

Yes, the position of a block on an incline can change over time. This is because the forces acting on the block, such as gravity and friction, can change over time. For example, if the incline surface is not perfectly smooth, the coefficient of friction may change as the block moves down the incline. Additionally, if the block is given an initial velocity, its position will change over time as it accelerates or decelerates. The exact position of the block at any given time can be calculated using the equations of motion and taking into account any changes in the forces acting on the block.

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