Normal Force and Acceleration

Oct 13, 2025 by wbrum.org 30 views

**1.8 A student weighing 500 N stands on a scale in an elevator moving down. When the scale reads 520 N, the elevator must be.**

Understanding the Problem

When a student weighing 500 N stands on a scale in an elevator moving down, the scale reading 520 N indicates an increase in the normal force exerted on the student. This situation can be analyzed using the concept of normal force and acceleration.

Normal Force and Acceleration

The normal force (N) exerted on an object is the force exerted by a surface on an object in contact with it. In the case of an elevator, the normal force is equal to the weight of the object (W) plus any additional force due to acceleration. The weight of the object is given by its mass (m) multiplied by the acceleration due to gravity (g).

Equation of Motion

The equation of motion for an object in an elevator is given by:

F = ma

where F is the net force acting on the object, m is its mass, and a is its acceleration.

Analysis of the Situation

When the scale reads 520 N, it means that the normal force exerted on the student is 520 N. Since the weight of the student is 500 N, the additional force due to acceleration is 20 N (520 N - 500 N).

Conclusion

To determine the direction of acceleration, we need to consider the direction of the additional force. Since the additional force is upward, the elevator must be accelerating downward. Therefore, the correct answer is:

C) decreasing

Q&A

Q1: What is the normal force exerted on the student when the scale reads 520 N?

A1: The normal force exerted on the student is 520 N.

Q2: What is the weight of the student?

A2: The weight of the student is 500 N.

Q3: What is the additional force due to acceleration?

A3: The additional force due to acceleration is 20 N (520 N - 500 N).

Q4: In which direction is the elevator accelerating?

A4: The elevator is accelerating downward.

Q5: What is the relationship between the normal force and acceleration?

A5: The normal force is equal to the weight of the object plus any additional force due to acceleration.

Q6: What is the equation of motion for an object in an elevator?

A6: The equation of motion for an object in an elevator is F = ma.

Q7: What is the direction of the additional force when the scale reads 520 N?

A7: The additional force is upward.

Q8: What is the conclusion based on the analysis of the situation?

A8: The elevator must be accelerating downward.

Q9: What is the correct answer?

A9: The correct answer is C) decreasing.

Q10: What is the significance of the normal force in this problem?

A10: The normal force is significant in this problem because it indicates the additional force due to acceleration, which helps determine the direction of acceleration.

Key Takeaways

The normal force exerted on an object is equal to its weight plus any additional force due to acceleration.
The direction of acceleration can be determined by the direction of the additional force.
The equation of motion for an object in an elevator is F = ma.
The normal force is significant in determining the direction of acceleration.

Conclusion

In conclusion, the correct answer is C) decreasing. The elevator must be accelerating downward when the scale reads 520 N. The normal force exerted on the student is 520 N, and the additional force due to acceleration is 20 N. The direction of acceleration can be determined by the direction of the additional force, which is upward in this case.