An elevator is pulled upward so it moves with increasing...

An elevator is pulled upward so it moves with increasing upward speed- the force exerted by the cable on the elevator is constant and greater than the downward gravitational force exerted by Earth. When the elevator is moving up medium-fast, the force exerted by the cable on the elevator changes abruptly to just balance the downward gravitational force of Earth - the sum of the forces that the cable and Earth exert on the elevator is now zero. Now what happens to the elevator? Explain. Represent your answer with position-versus-time and velocity-versus-time graphs. What assumptions did you make?

Key Concepts

Modeling Assumptions

In problem solving, assumptions such as treating forces as constant, neglecting friction and air resistance, and considering the system as ideal simplify the analysis. These assumptions allow focus on the fundamental dynamics without the complications of real-world imperfections.

Kinematic Graphs

Position-versus-time and velocity-versus-time graphs are essential tools in kinematics. A linear position-time graph indicates uniform motion with a constant velocity, while a horizontal line on a velocity-time graph signifies that the velocity remains constant over time, reflecting zero acceleration.

Force Equilibrium

When the sum of all forces acting on an object is zero, the object exhibits no acceleration according to Newton's first law of motion. This means the object will maintain its current velocity, which may be moving uniformly in a straight line.

Newton's Second Law

This law states that an object’s acceleration is directly proportional to the net force acting on it and inversely proportional to its mass. It provides the framework for analyzing how changes in force (or force equilibrium) will affect the motion of an object.

Transcript

00:01 So an elevator is pulled upwards, so it moves with an increasing upward speed.

00:05 And then at some point, and that's because the tension, the cable is bigger than the force that the earth is exerting.

00:13 And then at some point, it abruptly changes so that it's equal to the force that the earth is exerting.

00:18 So let's draw a picture of this.

00:21 Let's draw a motion diagram.

00:23 So it starts off and it's not moving.

00:26 Right? okay.

00:27 And then it goes faster and faster.

00:32 For some period of time, right? it's going faster and faster.

00:35 And then let's say, okay, now suddenly the force exactly equals the force of gravity.

00:41 So it doesn't accelerate.

00:43 And if it doesn't accelerate and it's already moving, then it's going to continue at the same speed.

00:49 Okay.

00:49 So these three lines are the same.

00:53 Here it's going faster and faster.

00:56 Here it's moving at the same speed here.

00:58 Okay.

01:01 So what happens to the elevator? so let's explain, right? okay, so we can explain this, right? so here it's accelerating, right? here it's got an upward acceleration.

01:15 And the reason for that is that we can draw the force diagram here, right? we've got the force that the earth is exerting and the force that the cable is exerting.

01:26 The cable force is more than the earth force, right? so it accelerates for this part.

01:31 In this region here, the force that the elevator is exerted.

01:34 Sorry, the force that the earth is exerting is the same as the force that the cable is exerting, right? so these guys are all congruent, right? and so if the upward force is exactly equal to the downward force, it just stops accelerating in the vertical direction.

01:54 Okay.

01:55 So our force diagram, that's what's going on here.

01:57 Here, this thing is bigger.

01:58 We have a bigger upward force and we've got the same downward force, right? and then when it stops accelerating, that just means the cable force is exactly equal to the.

02:07 Earth's force, right? like that...

Please give Ace some feedback