Find Relative Velocity: Acceleration on Inclined Plane

[ritwik06]

Homework Statement

There is an inclined plane(mass M) with inclination theta kept on a frictionless surface. A block of mass m is kept on it which is allowed to slide due to gravity. Find the accleration of the block with respect to to incline.

The Attempt at a Solution

The problem with this is that my answer does not match. So please guys just tell me if my answer is right or not?
If it proves out to be wrong, I shall post my working as well (its too big)My answer:

$$\vec{A}= \frac{(M-m)g sin \theta cos \theta}{M+m sin^{2}\theta} \hat{i}+ \frac{(M+m)g sin ^{2}\theta}{M+m sin^{2}\theta} \hat{j}$$

 

[ritwik06]

Homework Statement

There is an inclined plane(mass M) with inclination theta kept on a frictionless surface. A block of mass m is kept on it which is allowed to slide due to gravity. Find the accleration of the block with respect to to incline.

The Attempt at a Solution

The problem with this is that my answer does not match. So please guys just tell me if my answer is right or not?
If it proves out to be wrong, I shall post my working as well (its too big)


My answer:

$$\vec{A}= \frac{(M-m)g sin \theta cos \theta}{M+m sin^{2}\theta} \hat{i}+ \frac{(M+m)g sin ^{2}\theta}{M+m sin^{2}\theta} \hat{j}$$

I don't want you guys to directly tell me the answer. I have solved the question and I have got the following answer:
$$\vec{A}= \frac{(M-m)g sin \theta cos \theta}{M+m sin^{2}\theta} \hat{i}+ \frac{(M+m)g sin ^{2}\theta}{M+m sin^{2}\theta} \hat{j}$$

I just want you guys to tell me if th answer is correct or not. If not, I will show all the work that I did in order to get this answer.
My motive is only to save time.
Please help me.

 

[thomate1]

Your answer appears to be correct. The acceleration of the block on the inclined plane can be found using the formula a = (mgsinθ - μMgcosθ) / (m + Msin^2θ), where μ is the coefficient of friction between the block and the inclined plane. This equation takes into account the normal force and the force of friction acting on the block. It is important to note that the acceleration will vary depending on the angle of inclination and the masses of the block and the inclined plane. Additionally, the acceleration will decrease if the coefficient of friction increases, as this will create a larger opposing force on the block. It is always important to carefully consider all factors and variables when solving scientific problems.