1. Weight, Mass, and the Dreaded Elevator Problem

2. Mini-lab: Weight vs. Mass
Determine the mathematical relationship between an object’s weight and its mass.
Materials:
Electronic Scales
Triple Beam Balance
Multiple objects of different mass
Create a data table BEFORE starting the lab
Follow the instructions at the lab station.
Create a graph of force vs. mass
Compare the slope of your graph to g

3. Weight: True or False?
In your journal, re-write the statements below, state whether you think it is true or false, and provide 1-2 sentences of your reasoning.
The mass of an object depends on its location
The weight of an object depends on its location
Mass and weight are the same, but with different units.

4. Weight vs. Mass
Weight: The force that gravity exerts on an object with mass (m).
This force is what causes falling bodies to accelerate at 9.80 m/s2.
Weight is ALWAYS directed toward the center of the earth (down)
Remember, g = 9.80 m/s2
Units = Newtons

5. Apparent Weight
Apparent weight is the weight something appears to have as a result of an acceleration.
For example, if you were standing on a scale in an elevator, your apparent weight is the weight the scale would read.
So now for some conceptual practice…

6. Apparent Weight Practice…
Suppose you have a jet-powered flying platform that can move straight up and down. For each of the following cases, is you apparent weight equal to, greater than, or less then your true weight? Explain.
You are ascending and speeding up
You are descending and speeding up
You are ascending at a constant speed
You are ascending and slowing down
You are descending and slowing down
You are descending at a constant speed
Heavier
Lighter
Same

7. Constant Vertical Velocity
Example: A leaf falling at terminal velocity
Up is the positive (+) direction
𝑎=0 so… 𝐹 𝑁𝐸𝑇 =0
𝐹 𝑁𝐸𝑇 =0= 𝐹 𝑢𝑝 − 𝐹 𝑔
+ 𝐹 𝑔 𝐹 𝑔
𝐹 𝑢𝑝 = 𝐹 𝑔 (use the definition of weight)
𝐹 𝑢𝑝 =𝑚𝑔
F up = Fair
F g

8. Calculating Apparent Weight
Apparent weight can easily be calculated using the concept of net force.
For example, if you are standing on a scale when you are at rest, what forces are acting on you?
The force of gravity (your weight) and the force of the scale pushing back up (the normal force)
What is the net force in this situation?
0 N … you’re in static equilibrium

9. Draw a Free-body diagram for this situation:
Write out the vector equation:
Fscale = apparent weight
Fg = m g

10. Since this situation is in equilibrium,
Therefore,
which means the scale is reading the “True weight”
If the person standing on the scale has a mass of 65.0 kg, what is his weight?

11. Accelerating Upwards Example: A crate being lifted by a rope
Up is the positive (+) direction
𝑎 is↑so… 𝐹 𝑁𝐸𝑇 is↑
𝐹 𝑁𝐸𝑇 = 𝐹 𝑢𝑝 − 𝐹 𝑔
+ 𝐹 𝑔 𝐹 𝑔
𝐹 𝑁𝐸𝑇 + 𝐹 𝑔 = 𝐹 𝑢𝑝
𝑚𝑎+𝑚𝑔= 𝐹 𝑢𝑝 (using 2nd Law and the definition of weight)
𝐹 𝑢𝑝 =𝑚 𝑎+𝑔
F up = FT
F g

12. An Accelerating elevator…
If the elevator is accelerating upwards or downwards, then our problem becomes slightly longer…
For example, let’s say the elevator is accelerating upwards at a rate of 2.00 m/s2. What is now different from our first example?

13. Then write the vector equation:
Draw a free body diagram, including a vector off to the side indicating the direction of the net force:
Then write the vector equation:
Fscale = apparent weight
Fg = m g
Fnet

14. Since this situation is NOT in equilibrium, the following is ALSO TRUE:
Using substitution, we can determine the size of the apparent weight (the reading on the scale):

15. Accelerating Downwards
Example: A sky diver in free fall
Up is the positive (+) direction
𝑎 is↓so… 𝐹 𝑁𝐸𝑇 is↓
− 𝐹 𝑁𝐸𝑇 = 𝐹 𝑢𝑝 − 𝐹 𝑔
+ 𝐹 𝑔 𝐹 𝑔
−𝐹 𝑁𝐸𝑇 + 𝐹 𝑔 = 𝐹 𝑢𝑝
−𝑚𝑎+𝑚𝑔= 𝐹 𝑢𝑝 (using 2nd Law and the definition of weight)
𝐹 𝑢𝑝 =𝑚 𝑔−𝑎
F up = Fair
F g

16. Another Accelerating elevator…
Now let’s say the elevator is accelerating downwards at a rate of 2.00 m/s2. Draw the free-body diagram for this situation:
Fscale = apparent weight
Fg = m g
Fnet

17. Again, we can write the vector equations…
HOWEVER: the net force is now DOWN, so it (and the acceleration) is therefore a negative value…
Using substitution, we can determine the size of the apparent weight (the reading on the scale):

18. Now You Try!
Determine the apparent weight of a 67 kg man standing in an elevator when the elevator is:
At rest
Ascending and speeding up at a rate of 1.5 m/s2
Ascending and slowing down at a rate of -1.2 m/s2