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In example 4.9, What Does the Bathroom Scale Read in an Elevator?, why does the normal force exceed the person's weight?
Group of answer choices

because the person is pushing down on the weighing scale

because the elevator is moving

because there has to be a net force upward in order for there to be an acceleration upward

In example 4.9, where a person stands on a bathroom scale in an accelerating elevator, the reason the normal force (which is what the scale reads) exceeds the person’s weight is:

**Because there has to be a net force upward in order for there to be an acceleration upward.**

### Explanation:
When the elevator accelerates upward, Newton's second law (\( F = ma \)) requires a net upward force to create this upward acceleration. The forces acting on the person are:
1. The gravitational force (weight), \( w = mg \), acting downward.
2. The normal force \( N \), acting upward, which is the force the scale exerts on the person.

To achieve upward acceleration, the upward normal force must be greater than the downward gravitational force, so:
\[
N = mg + ma
\]
where \( a \) is the upward acceleration of the elevator. The scale reads this normal force, which is now larger than the weight alone due to the additional acceleration term. 

This setup creates a net upward force, leading to the perception of an increased weight reading on the scale.

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Would you like further details or have any questions?

Here are five related questions to expand your understanding:
1. What would the scale read if the elevator were accelerating downward?
2. How does the scale reading change if the elevator moves at a constant speed (no acceleration)?
3. Why does the person feel "heavier" when the elevator accelerates upward?
4. How would Newton's third law apply if a second person were standing on the scale in the same elevator?
5. How would the scale reading change if the elevator cable were cut (free fall situation)?

**Tip:** Remember, when analyzing forces, always separate weight (gravitational force) from the normal force, which depends on the context, like acceleration in this case.

In example 4.9, What Does the Bathroom Scale Read in an Elevator?, why does the normal force exceed the person's weight? Group of answer choices: because the person is pushing down on the weighing scale, because the elevator is moving, or because there has to be a net force upward in order for there to be an acceleration upward.

Explore why the normal force on a bathroom scale exceeds a person's weight in an accelerating elevator. This example demonstrates Newton's second law (F = ma), where a net force upward results in an increased normal force reading. Learn about key physics concepts like normal force, acceleration, and Newton's laws. Ideal for high school physics students in Grades 11-12.

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