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(III) An inclined plane, fixed to the inside of an elevator,makes a $32^{\circ}$ angle with the floor. A mass $m$ slides on theplane without friction. What is its acceleration relative tothe plane if the elevator $(a)$ acceleration relative to(b) accelerates downward at $0.50 g,(c)$ falls freely, and$(d)$ moves upward at constant speed?

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a) $7.79 \mathrm{m} / \mathrm{s}^{2}$down the incline.b) $2.60 \mathrm{m} / \mathrm{s}^{2}$ down the incline.c) $0 \mathrm{m} / \mathrm{s}^{2}$d) $5.19 \mathrm{m} / \mathrm{s}^{2}$ down the incline.

Physics 101 Mechanics

Chapter 6

Gravitation and Newton's Synthesis

Physics Basics

Newton's Laws of Motion

Applying Newton's Laws

Gravitation

Cornell University

Simon Fraser University

Hope College

University of Winnipeg

Lectures

03:43

In physics, dynamics is the branch of physics concerned with the study of forces and their effect on matter, commonly in the context of motion. In everyday usage, "dynamics" usually refers to a set of laws that describe the motion of bodies under the action of a system of forces. The motion of a body is described by its position and its velocity as the time value varies. The science of dynamics can be subdivided into, Dynamics of a rigid body, which deals with the motion of a rigid body in the frame of reference where it is considered to be a rigid body. Dynamics of a continuum, which deals with the motion of a continuous system, in the frame of reference where the system is considered to be a continuum.

03:55

In physics, orbital motion is the motion of an object around another object, which is often a star or planet. Orbital motion is affected by the gravity of the central object, as well as by the resistance of deep space (which is negligible at the distances of most orbits in the Solar System).

01:40

An object is on a friction…

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An elevator ascending with…

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A particle slides down a s…

02:12

A body projected horizonta…

00:53

A block of mass 3.5 kg sli…

03:19

03:23

A block of mass $3 \mathrm…

01:41

A block is projected up a …

02:39

A body is moving down a lo…

03:12

02:22

A lift is moving downwards…

01:32

07:19

(II) The crate shown in Fi…

01:50

An inclined plane makes an…

So it's a first draught Free Bart, A diagram. Um, it's okay. My apologies. Yeah. And so we have a mass here Perpendicular to the surface will always be normal force. Going straight down will always be the force of gravity. And then here this is the direction of it the acceleration. And we're going to define our new Cartesian access. This should be a riot axis, and this would be our X axis. So essentially here, another reading to save mine. So essentially here were defining a new Cartesian access in order to make evaluating it easier were going to say that the effective acceleration due to gravity would be equal to the acceleration of gravity G plus the acceleration of the elevator. So for part A when we when the question is telling us that the acceleration of the elevator equals 0.5 g, we can say that the effective exploration to the gravity would be equal to 1.5 s. So we can say that the relative velocity is going to be equal to the effective acceleration due to gravity times Sign of Fada, where this angle here would be fatal. We can say that this is going to be equal to 1.5 times 9.8 time's sign of 30 two degrees. And so the relative acceleration is going to be able to 7.79 meters per second squared. So this would be our final answer for apart, eh? For party. Now, the acceleration of the elevator yeah, is equaling negative 0.5 g. So this means that the effective acceleration due to gravity would be equal to only 0.5 g. And so we can say that the relative acceleration will be equal to the, um quick, it's to say, 0.5 times 9.8 times again sign of 32 degrees. And this is giving us 2.60 meters per second squared. Now, um, my apologies. Yeah, just wanted to confirm the units for part. See, we know that the acceleration of the elevator equals negative g. So here the effective grabbed thie effective exploration to the gravity's actually zero meters per second squared, which means that the relative acceleration will, of course, simply be again zero meters per second squared. So, at this point for party, we know that the acceleration of the elevator here equals zero. So the effective acceleration due to gravity will simply be equal to the acceleration due to gravity. And again, the relative acceleration will be equal to 9.8 sign of 32 degrees. So the of the relative acceleration will be equal to 5.19 meters per second squared. So this would be a final answer for Part D. Our final answer for part see and final answer for part B. That is the end of the solution. Thank you for watching.

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