Solving this question from an inertial FOF

[EddiePhys]

Homework Statement

Need to find the time t taken for m to reach the bottom

Homework Equations

F = ma

The Attempt at a Solution

[/B]
I don't know how to go about solving this from an inertial frame. In my view, the only two forces acting on this block are mg, which has a mgsin(theta) component along the plane and the normal force acting on the block however, the normal force has no component along the plane and hence it wouldn't affect the acceleration. This gives an acceleration of gsin(theta) which I know is the wrong answer. This question is easy to solve when we're in the FOF of the elevator ie an accelerated frame but I'm not able to figure out how to solve for the acceleration from an inertial frame. Once the acceleration is found the rest of the problem is pretty straightforward.

 

[drvrm]

Homework Statement

View attachment 100178
Need to find the time t taken for m to reach the bottom

Homework Equations

F = ma

The Attempt at a Solution

[/B]
I don't know how to go about solving this from an inertial frame. In my view, the only two forces acting on this block are mg, which has a mgsin(theta) component along the plane and the normal force acting on the block however, the normal force has no component along the plane and hence it wouldn't affect the acceleration. This gives an acceleration of gsin(theta) which I know is the wrong answer. This question is easy to solve when we're in the FOF of the elevator ie an accelerated frame but I'm not able to figure out how to solve for the acceleration from an inertial frame. Once the acceleration is found the rest of the problem is pretty straightforward.

pl. frame your question more clearly - in inertial frame that is when elevator acceleration is zero
draw a free body diagram of forces acting on mass m and find out acceleration ; similarly draw draw a free body diagram in accelerated frame - i can not understand how it is easy in accelerated frame and how it is difficult in inertial one ?

 

[EddiePhys]

pl. frame your question more clearly - in inertial frame that is when elevator acceleration is zero
draw a free body diagram of forces acting on mass m and find out acceleration ; similarly draw draw a free body diagram in accelerated frame - i can not understand how it is easy in accelerated frame and how it is difficult in inertial one ?

How is the acceleration zero in the inertial frame?

 

[drvrm]

How is the acceleration zero in the inertial frame?

If a frame is accelerating then the FOF is non inertial and one can not write down correctly the Newton;s Equation - so it is rendered inertial by applying a reverse pseudo force so that frame's observation can be written by a new relation F(effective) =m.acceleration
for example a person is standing in an elevator on a weighing machine.
1. if the elevator is at rest or moving with uniform velocity his weight W will be correctly shown on weighing machine.
2. Imagine elevator to move upward with say acceleration a - then observe the weighing machine - it will show a weight of W + M.a , the man will become heavier.effectively an inertial observation is being done by observing a reverse effective force acting on the body.
3. if we apply a reverse acceleration -a to the lift -the lift becomes an inertial frame but the force operating will be changed to F(effective)= F +Ma
This is called a pseudo force generated due to frame's acceleration.
In your problem apply an acceleration a(0) -the acceleration of the elevator in reverse /downward direction and then write the Newtons equation
so your free body diagram will have an additional pseudo force operating down ward.
perhaps i could make myself clear to you.
as the man became heavier your mass will be pulled down by m(g+a(0) ) in an inertial FOF

 

[EddiePhys]

If a frame is accelerating then the FOF is non inertial and one can not write down correctly the Newton;s Equation - so it is rendered inertial by applying a reverse pseudo force so that frame's observation can be written by a new relation F(effective) =m.acceleration
for example a person is standing in an elevator on a weighing machine.
1. if the elevator is at rest or moving with uniform velocity his weight W will be correctly shown on weighing machine.
2. Imagine elevator to move upward with say acceleration a - then observe the weighing machine - it will show a weight of W + M.a , the man will become heavier.effectively an inertial observation is being done by observing a reverse effective force acting on the body.
3. if we apply a reverse acceleration -a to the lift -the lift becomes an inertial frame but the force operating will be changed to F(effective)= F +Ma
This is called a pseudo force generated due to frame's acceleration.
In your problem apply an acceleration a(0) -the acceleration of the elevator in reverse /downwarddirection and then write the Newtons equation
so your free body diagram will have an additional pseudo force operating down ward.
perhaps i could make myself clear to you.
as the man became heavier your mass will be pulled down by m(g+a(0) ) in an inertial FOF

I understand what pseudo force is and how it works. What I was saying is that in the inertial frame the acceleration is not zero. In the non inertial frame ie the frame of the elevator the acceleration is zero.
Anyway, I've tried solving this question from an inertial i.e ground frame but I'm not able to. Could you help? Maybe by showing me a free-body diagram?

 

[drvrm]

I understand what pseudo force is and how it works. What I was saying is that in the inertial frame the acceleration is not zero. In the non inertial frame ie the frame of the elevator the acceleration is zero.
Anyway, I've tried solving this question from an inertial i.e ground frame but I'm not able to. Could you help? Maybe by showing me a free-body diagram?

May I ask you a question?
What do you understand by an Inertial Frame reference?

The frames in Which the Law of Inertia holds good are called "Inertial Frames" or Inertial observers with Their own FOR.
The man on the ground and the Man in the elevator both become Inertial when artificially a "pseudo force " is applied and elevator becomes non accelerated i.e. either at rest or moving with uniform speed.

All frames either at rest or moving with Uniform velocity are Inertial frames.
for example the man in the elevator weighs say W at the scales at the ground and in moving elevator with Uniform velocity will weigh the same W kg. the acceleration due to gravity is same on Earth as well as in elevator moving with uniform speed. as it is generated due to a physical Law of gravitation and is not due to motion of frames.

The pseudo force is needed only when the frames accelerate or decelerate and the Newton's Laws are to be applied..

 

[conscience]

Hi EddiePhys ,

I don't know how to go about solving this from an inertial frame. In my view, the only two forces acting on this block are mg, which has a mgsin(theta) component along the plane and the normal force acting on the block however, the normal force has no component along the plane and hence it wouldn't affect the acceleration.

Good .

If you can solve this problem in non inertial frame of elevator , then solving it from the ground frame will not be difficult for you .

In Newton's II law i.e ΣF = Ma , what does 'a' represent ?

 

[EddiePhys]

Hi EddiePhys ,
Good .

If you can solve this problem in non inertial frame of elevator , then solving it from the ground frame will not be difficult for you .

In Newton's II law i.e ΣF = Ma , what does 'a' represent ?

acceleration of the body.
I've managed to solve it from a noninertial frame where an ma₀ pseudo force is applied downwards. I don't know how to do it from the ground frame.

 

[conscience]

acceleration of the body.

net acceleration

I've managed to solve it from a noninertial frame where an ma₀ pseudo force is applied downwards. I don't know how to do it from the ground frame.

I understand what you are looking for .

Suppose acceleration of an object when measured from a moving reference frame 'X' is $\vec{a_1}$ and acceleration of 'X' as measured from the ground/lab frame is $\vec{a_2}$ , then what is the net acceleration of the object ?