Apparent Weight in an Elevator How does your weight change in an elevator? Your apparent weight is equal to the normal force between your feet and the ground. The normal force will act to balance whatever other forces are applied to your body in the direction of the ground. This includes the force of gravity due to the earth, and the force applied by the elevator floor. You may choose a volunteer from your group and you may all share the data. Please use the elevator closest to Ryan Lecture Hall for this experiment. Before you start this experiment, you will need to determine your volunteer’s mass. Stand on the Vernier Force Plate, measure the volunteer’s weight in Newtons, and record it here: 59. Draw a Free Body Diagram for the volunteer on the scale in the lab. Calculate the volunteer’s mass from: EFy = may.
Free Body Diagram and Explanation: Apparent Weight in an Elevator
Step 1: Determine the volunteer’s mass
The weight measured on the Vernier Force Plate in the lab is:Fg=59 NF_g = 59 \, \text{N}Fg=59N
The gravitational force FgF_gFg is related to mass by Newton’s second law:Fg=mgF_g = mgFg=mg
Where:
- FgF_gFg is the weight in Newtons (N),
- mmm is mass in kilograms (kg),
- ggg is the acceleration due to gravity (9.8 m/s²).
Solving for mass:m=Fgg=599.8≈6.02 kgm = \frac{F_g}{g} = \frac{59}{9.8} \approx 6.02 \, \text{kg}m=gFg=9.859≈6.02kg
So, the volunteer’s mass is approximately 6.02 kg.
Step 2: Free Body Diagram in the Lab (At Rest)
When standing on the scale in the lab (not accelerating), the elevator is stationary or moving at constant velocity. The two vertical forces acting on the person are:
- Gravitational force (Weight): Fg=mgF_g = mgFg=mg, acting downward.
- Normal force (Apparent weight): FNF_NFN, exerted by the scale, acting upward.
Since the person is at rest or moving with constant velocity, net force is zero:ΣFy=may=0⇒FN−mg=0⇒FN=mg\Sigma F_y = ma_y = 0 \Rightarrow F_N – mg = 0 \Rightarrow F_N = mgΣFy=may=0⇒FN−mg=0⇒FN=mg
Therefore, the scale reads the actual weight, which is 59 N.
Step 3: Apparent Weight in an Accelerating Elevator
Now suppose the elevator accelerates. The apparent weight is the normal force FNF_NFN, not the actual weight. Let’s apply Newton’s Second Law:ΣFy=may=FN−mg⇒FN=m(g+ay)\Sigma F_y = ma_y = F_N – mg \Rightarrow F_N = m(g + a_y)ΣFy=may=FN−mg⇒FN=m(g+ay)
- If the elevator accelerates upward, ay>0a_y > 0ay>0: apparent weight increases.
- If the elevator accelerates downward, ay<0a_y < 0ay<0: apparent weight decreases.
- If ay=−ga_y = -gay=−g (free fall), then FN=0F_N = 0FN=0: the person feels weightless.
Explanation
When you are in an elevator, your actual weight (gravitational force) remains constant and is given by mgmgmg, where mmm is your mass and ggg is the acceleration due to gravity. However, what you feel—and what a scale reads—is your apparent weight, which corresponds to the normal force (FNF_NFN) exerted by the floor.
In a stationary elevator or one moving at constant speed, the forces are balanced: the upward normal force exactly cancels the downward gravitational force, and the apparent weight equals the real weight. But when the elevator accelerates, things change.
If the elevator accelerates upward, the floor must push up harder to accelerate you, so the normal force increases. You feel heavier, and the scale shows a higher value than your actual weight. Conversely, if the elevator accelerates downward, the floor doesn’t push up as strongly, so the normal force (and thus the scale reading) decreases. You feel lighter.
In the extreme case where the elevator is in free fall (accelerating downward at 9.8 m/s²), the normal force becomes zero. You and the scale fall at the same rate, and no contact force exists between your feet and the floor. This is called apparent weightlessness, even though gravity is still acting on you.
This concept helps explain why astronauts in orbit feel weightless—because they’re in constant free fall, not because gravity disappears. Similarly, this lab experiment using the force plate helps us understand how Newton’s laws govern everyday situations, such as elevator rides.
