Hard kinematics problem: Block pushed onto a moving conveyor belt

[IamVector]

$\frac 2 {\sqrt 5} m/s$ is the answer I get.

In general the minimum speed is $v_b \cos \theta'$, where $v_b$ is the speed of the belt and $\theta'$ is the angle of motion relative to the belt.

can you please explain further will be a great help

 

[IamVector]

$\frac 2 {\sqrt 5} m/s$ is the answer I get.

In general the minimum speed is $v_b \cos \theta'$, where $v_b$ is the speed of the belt and $\theta'$ is the angle of motion relative to the belt.

is my approach right just want to confirm??

 

[PeroK]

can you please explain further will be a great help

That's what comes out of the algebra and calculus. I suspect the geometric approach could be generalised.

 

[IamVector]

That's what comes out of the algebra and calculus. I suspect the geometric approach could be generalised.

is my approach correct?? otherwise I will try it with different approach cause sometimes answer is correct approach is wrong

 

[PeroK]

is my approach correct?? otherwise I will try it with different approach cause sometimes answer is correct approach is wrong

I haven't seen your approach.

 

[IamVector]

I haven't seen your approach.

ok , so i got this equation (-1+μ gt/(5^1/2))i + (2-2μ gt/(5^1/2))j so to convert it into lab frame or ground frame I added 1m/s ie velocity of belt then I took the mod of the resultant vector ie (-1+μ gt/(5^1/2))i + (2-2μ gt/(5^1/2))j which in return formed a quadratic in μgt now we were asked to find the minimum vector so it will be minimum when the value of quadratic will be minimum so by differentiating i found the min val to be 4/5 thus on sqrt gives 2/(5^1/2)

 

[IamVector]

I haven't seen your approach.

I am preparing for Olympiads a word of advice will be appreciated and are the level of difficulty of questions I am doing sufficient??

 

[PeroK]

I am preparing for Olympiads a word of advice will be appreciated and are the level of difficulty of questions I am doing sufficient??

I don't know. Try this one:

https://www.physicsforums.com/threads/find-initial-acceleration-in-a-system.985009/

Don't take all my advice on that thread! Looking at energy wasn't much use. Forces and torques.

 

[IamVector]

I don't know. Try this one:

https://www.physicsforums.com/threads/find-initial-acceleration-in-a-system.985009/

Don't take all my advice on that thread! Looking at energy wasn't much use. Forces and torques.

Is it g/2? I am not sure

 

[PeroK]

Is it g/2? I am not sure

That's a quite a hard problem I think. You can't just guess that the answer is $g/2$ or $3g/13$ or whatever. You have to work it out.

 

[IamVector]

That's a quite a hard problem I think. You can't just guess that the answer is $g/2$ or $3g/13$ or whatever. You have to work it out.

Well I took the component of mg acting on rod but I doubt it's a right approach.