Understanding the Dynamics of Acceleration in the Wedge Problem

In summary, the conversation discusses the acceleration of a block with respect to ground and its relation to the acceleration of a wedge. It is determined that the acceleration of the block with respect to the ground is equal to the sum of its horizontal and vertical components, which are both equal to 2asin(α/2). This does not match any of the given options and could potentially be due to a typo in the problem.
  • #1
vaibhav garg
16
0
In the adjoining figure if acceleration of M with respect to ground is a, then
A) Acceleration of m with respect to M is a
B) Acceleration of m with respect to ground is asin(α/2)
C) Acceleration of m with respect to ground is a
D) Acceleration of m with respect to ground is atan(α)

The 2nd question in the image below
IMG_20160406_231223460.jpg

The acceleration of m in the vertical direction should be atan(α) by using length constant relation and in the horizontal direction it should be same as the wedge that is a. therefore the resultant should be asec(α), what am i doing wrong here ?
 
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  • #2
vaibhav garg said:
In the adjoining figure if acceleration of M with respect to ground is a, then
A) Acceleration of m with respect to M is a
B) Acceleration of m with respect to ground is asin(α/2)
C) Acceleration of m with respect to ground is a
D) Acceleration of m with respect to ground is atan(α)

The 2nd question in the image below
View attachment 98702
The acceleration of m in the vertical direction should be atan(α) by using length constant relation and in the horizontal direction it should be same as the wedge that is a. therefore the resultant should be asec(α), what am i doing wrong here ?
Are you sure? The wedge moves horizontally and the block slides down along it, so it moves both horizontally and vertically with respect to the ground.
 
  • #3
ok I get what you are saying, so if we take A to be the acceleration of the block wrt to M. therefore it's acceleration with respect to the ground will be
(a - Acosα) horizontally and Asinα vertically. But now how do I find a relation between A and a
 
  • #4
vaibhav garg said:
ok I get what you are saying, so if we take A to be the acceleration of the block wrt to M. therefore it's acceleration with respect to the ground will be
(a - Acosα) horizontally and Asinα vertically. But now how do I find a relation between A and a
If the wedge moves by x to the left, the length of the rope between the wall and pulley becomes shorter by x.So the other piece along the wedge becomes longer by the same length x. What does it mean for the accelerations a and A?
 
  • #5
that they are both equal. so when we add the the two components it would give the answer to be B. Thanks ehlid :)
 
  • #6
vaibhav garg said:
that they are both equal. so when we add the the two components it would give the answer to be B. Thanks ehlid :)
I got a bit different result, but it might have been my error, or a typo in the problem text. Show your work, please.
 
  • #7
the horizontal component would be (a-acosα) which is equal to 2asin2α/2 the vertical component 2asin(α/2)cos(α/2) the resultant would be 2asin(α/2)... I am sorry :P but this dosen't matches any of the options
 
  • #8
I got the same result, and I do not see any flaw. Sometimes there are typos in the written texts.
 

1. What is the Dynamics wedge problem?

The Dynamics wedge problem is a physics problem that involves a wedge-shaped object on an inclined plane. The goal is to determine the motion and forces acting on the object.

2. How is the Dynamics wedge problem different from other physics problems?

The Dynamics wedge problem is unique because it involves a non-uniform object on an inclined plane, which makes it more challenging to solve compared to other physics problems.

3. What are the key principles used to solve the Dynamics wedge problem?

The key principles used to solve the Dynamics wedge problem are Newton's laws of motion, the concept of static and kinetic friction, and the principle of conservation of energy.

4. How can the Dynamics wedge problem be applied in real-life situations?

The Dynamics wedge problem can be applied in various real-life situations such as determining the motion and forces acting on a car driving up a steep hill or a heavy object being pushed up an inclined ramp.

5. What are some common mistakes when solving the Dynamics wedge problem?

Some common mistakes when solving the Dynamics wedge problem include not considering the direction of forces, not taking into account the non-uniform shape of the wedge, and not properly applying the equations of motion.

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