ShowMe - Elevator

Free Body Diagrams are automatically created and appear as blue and green force vectors drawn on the left side of the elevator. The blue vector represents the normal force of the elevator pushing up on the occupant (N), while the green vector represents the force of gravity or weight pulling down on the occupant (W). A "net force" indicator on the right of the elevator gives you a visual representation of the sum of these two forces.

1. Note that as you adjust the mass of the occupant, both N and W change in response to this and, as long as the elevator is not accelerating, will have identical lengths. Try changing the mass to observe this.

2. The free body diagram can easily be turned into an equation: . Since the net force is zero in this initial setup, you can see that the normal force of the elevator on the occupant is precisely equal to the weight of the occupant. If the person is standing on a scale, then the scale would be providing the normal force and this in turn would imply that the scale reading would equal the weight of the person.
3. For example, set the mass of the occupant to equal 80 kg. Since the scale reading should equal the weight of the person, you should see that . You can confirm this by checking the scale reading information that is given in the output window at the upper left area of the applet ().

4. To continue the example, adjust the acceleration to 4 m/s² and click "Up". The occupant (and elevator) will begin to accelerate upward. Since a force is required for an acceleration, you should expect to see this reflected in the free body diagram. Your diagram should look like the one shown below. This also implies the following equation:. Since we know that a = 4 m/s², we can solve this equation for N . This gives us .
   If we insert the correct values, we find that N has now grown to (80 kg) (4 m/s²)+784.8 N = 1104.8 N. This is reflected in the slightly longer arrow shown for N in the FBD.

5. Notice that after a few seconds of motion, the elevator begins to coast. At this point, the net force must once again drop to zero and we also see that N = W and that the scale reading is once more equal to the weight.

6. Finally, the elevator begins to decelerate. Now the net force on the occupant is in the opposite direction and the free body diagram implies the following equation: .

If we solve for N we find
, and N = 464.8 N. This means that the scale reading has dropped, and the occupant's apparent weight is now lower.

1. It is very easy to display position, velocity, and acceleration time graphs for the elevator. For example, set the acceleration of the elevator at 3 m/s² and click "Up". The elevator will accelerate upward, coast, and then decelerate to a complete stop. Click "View Graph", and select time for the x-axis and displacement for the y-axis options. The position-time graph for this motion is shown below.
2. You now may use the various graphing tools to examine the graph. For example, use the slope tool to measure the slope of the position-time graph for any time during the motion of the elevator. When you press this button, a blue slope arrow appears on the curve. You can move this arrow along the curve by dragging it with the mouse. The slope of a position-time graph tells you its velocity, so by using this tool you can determine the velocity of the elevator. As an example, find the slope at t = 32 s. Either drag the blue slope arrow along the curve until the time (x-axis value) equals 32 s, or double-click on the slope button and enter 32 s in the text box that opens. The slope appears in the "output" window of the graph and indicates a value of 78.0 m/s. You can confirm this by either re-running the applet and noting the velocity when t = 32 s or by creating a velocity-time graph.

3. Make a velocity-time graph for this motion, similar to the sample graph shown below. Again, you can use graphing tools to examine this graph. It also is easy to see that the elevator's motion consists of 3 phases: speeding up, coasting, and decelerating. By using the slope tool, you could measure the accelerations in the 3 phases and compare them with the values found by plotting an acceleration-time graph.

1. A very useful feature of the graphing tool is the ability for the user to define his or her own functions. For example, we could graph the changing kinetic energy of the occupant in the elevator as the elevator moves through its complete motion.

   To illustrate this, set the mass of the occupant to 80 kg and the acceleration to 4 m/s². Since kinetic energy is given by the expression , we can create this by clicking the data collection button and choosing the select data option.
   
   

2. A new dialogue box opens that lists the variables currently available to you. Choose "Add" and then proceed to fill out the template that opens (see the next diagram).
   

3. A new variable (E_k) has been defined by the equation 0.5*80*v*v. (Alternately, you could have written this as 40*v*v). When you click "OK", this variable will now become active and can be plotted.

4. The graph of kinetic energy vs. time is shown on the right. To create this graph, choose the new variable E_k for the y-axis and time for the x-axis.
5. You can enter other functions and their graphs by following the steps described above.