(III) An inclined plane, fixed to the inside of an elevator, m...

Question

(III) An inclined plane, fixed to the inside of an elevator, makes a 38° angle with the floor. A mass m slides on the plane without friction. What is its acceleration relative to the plane if the elevator
(c) falls freely, and

(c) falls freely, and

Accepted Answer

Welcome back. Everyone in this problem. A helicopter is flying still in the air, an inclined plane is fixed to the floor of the helicopter inside it making an under an angle of 35 degrees with the floor. A book of mass M slides without friction on the inclined plane. If the helicopter starts to fall freely, what would the acceleration of the book be relative to the plane? For our answer choices? A says it's negative 11 m per second squared, B 0 m per second squared, C 9.81 m per second squared and D 11 m per second squared. No, to understand our problem. Let's try to visualize what's going on. So we're saying inside our helicopter, we have an inclined plane. Let me make that a bit bigger E and for this incline plane, it's inclined at an angle 35 degrees. Let's let theta represent 35 degrees for some simplicity in the diagram. And now we're looking at our book of a mass M that's sliding down the incline when the helicopter starts to fall freely. Now for this book, first of all, the weight of the book would be acting vertically and that weight F would be equal to MG. Now, for it, let's consider the helicopter with an acceleration of a OK. So for an observer in the helicopter, everything would appear to be going down with an acceleration of a. So for so for an observer in the helicopter, everything would experience a corresponding force. And for this corresponding force recall, Newton's second law tells us that force is directly proportional to acceleration by the formula F equals mass multiplied by acceleration. So this corresponding force F OK? Or let's in this case to differentiate it, let's call it F prime would be equal to the mass of the book. M multiplied by the acceleration of the helicopter. OK? And for if it's we, that should also be a capital M. Now, for this block for this book, OK. We also know that it has a normal force acting against the book. And let's call that FN. So the forces acting on the block in the free body diagram are FF prime and FN. No F and F prime both are acting in a downward direction. So they both make an angle of theta degrees. Let me put that in here an angle of theta degrees with the normal. OK. So let me draw that, I wanna draw that as best as I can. So they make an angle of 30 degrees with the normal. OK? And no FN being normal with respect to the incline, the component of FN along the incline is zero and the components of the forces acting along the incline in this direction, OK. Namely here and here, OK. These forces the force uh the force drawn in black, let me put that back as a component of F would be F uh let me read it properly would be F sign theater. OK? And in blue, the component of F prime, we're talking about the helicopter would be F prime sign theater. So those are forces acting. And again, we said we want to find acceleration of the book relative to the plane. So in red, let's let that a net acceleration be A R. Now, how are we going to figure that out? Well, we spoke about something earlier that can help us again, recall Newton's second law that says force equals mass multiplied by acceleration in this case or rather net force, I should say in this case, the net force acting in the direction of the incline is going to be um F. So I didn't put that in red, F prime sine theta plus F sign theater, both are acting in the same direction and both of those are going to be equal to the mass of the book M multiplied by the acceleration of the book R. OK. Based on Newton's second law. Now, if we think about it, we know what F is in terms of the mass and we know what F prime is in terms of our mass. So we can substitute here. So by substituting OK, we can replace F prime with the mass multiplied by the acceleration of the helicopter. So that's M sine theta plus F, the weight of the book MGS sign theta is equal to M multiplied by A R. All of them have M in common. So we can cancel out M and we end up with ar being equal to a sine theta plus G sine theta. Notice both of terms have sine theta in common. So we can factor out sine theta to be left with a G multiplied by sine theta. And now we are almost there to figuring out the acceleration of our book acceleration of the book relative to the plane. We know what the acceleration due to gravity G is, but we don't know what the acceleration of our helicopter is. Now, what can we use here? Let's look back on the information that we have no recall. OK. That in this scenario, the helicopter starts to fall freely. What do we know about freefall? Well, in freefall, our acceleration would be opposite to the acceleration due to gravity. It would be the same as the acceleration due to gravity. So in other words, in freefall, yeah, in free flight, A equals negative G. So if this is our acceleration due to the or if this is the value of A, then if we substitute it into our formula, that means the acceleration of the book is going to be equal to negative G plus G multiplied by the sine of our anger theta. No negative G plus G zero. So that means A is going to be equal to zero, sine theta and zero multiplied by sine theta must be equal to zero. So the acceleration of our book is going to be 0 m per second squared. If we look back on our answer, choices B is the correct answer. Thanks a lot for watching everyone. I hope this video helped.

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(III) An inclined plane, fixed to the inside of an elevator, makes a 38° angle with the floor. A mass m slides on the plane without friction. What is its acceleration relative to the plane if the elevator
(c) falls freely, and

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Struggling with Physics?

(III) An inclined plane, fixed to the inside of an elevator, makes a 38° angle with the floor. A mass m slides on the plane without friction. What is its acceleration relative to the plane if the elevator(c) falls freely, and

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(III) An inclined plane, fixed to the inside of an elevator, makes a 38° angle with the floor. A mass m slides on the plane without friction. What is its acceleration relative to the plane if the elevator
(c) falls freely, and