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Let's work through each part of the problem based on the image you've provided:

### Known Information:
- Rogan's mass \( m = 60 \, \text{kg} \)
- Rogan's apparent weight \( F_{\text{apparent}} = 535 \, \text{N} \)
- Gravitational acceleration \( g = 9.8 \, \text{m/s}^2 \)

#### a. Draw his free body diagram:
In a free body diagram of Rogan in the elevator, there are two main forces acting on him:
1. **Gravitational force** \( F_g = mg \), acting downwards.
2. **Normal force** \( N \), which represents the apparent weight, acting upwards.

Since Rogan’s apparent weight differs from his actual weight, the elevator must be accelerating either upwards or downwards.

#### b. Determine the acceleration of the elevator:
First, calculate Rogan's actual weight using \( F_g = mg \):
\[
F_g = 60 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 588 \, \text{N}
\]

The apparent weight is given as \( F_{\text{apparent}} = 535 \, \text{N} \), which is less than the actual weight. This suggests the elevator is accelerating **downwards**.

Now, we can use the equation for apparent weight:
\[
F_{\text{apparent}} = m(g - a)
\]
Where \( a \) is the acceleration of the elevator.

Substituting the known values:
\[
535 = 60 \times (9.8 - a)
\]
Solve for \( a \):
\[
535 = 588 - 60a
\]
\[
60a = 588 - 535 = 53
\]
\[
a = \frac{53}{60} \approx 0.883 \, \text{m/s}^2
\]

Thus, the elevator is accelerating downwards with an acceleration of \( 0.883 \, \text{m/s}^2 \).

#### c. Describe two different possible motions of the elevator:
1. **The elevator could be moving downwards and accelerating**: This would explain the reduction in apparent weight because the normal force is less than the gravitational force.
2. **The elevator could be moving upwards and decelerating**: In this scenario, the elevator is still going upwards but slowing down, causing the apparent weight to decrease.

Would you like further details or clarification?

### Related Questions:
1. How does the direction of acceleration affect the apparent weight?
2. What would the apparent weight be if the elevator were accelerating upwards?
3. How would the problem change if the elevator were in free fall?
4. What forces act on Rogan when the elevator is stationary?
5. Can you explain why apparent weight increases or decreases with acceleration?

### Tip:
Always check the direction of acceleration when calculating apparent weight. If the apparent weight is less than the actual weight, the acceleration is downward, and if it's greater, the acceleration is upward.

Rogan (m = 60 kg) is riding in an elevator. His apparent weight is 535 N.
a. Draw his free body diagram.
b. Determine the acceleration of the elevator.
c. Describe two different possible motions of the elevator.

Learn how to calculate the acceleration of an elevator by analyzing apparent weight and forces. This problem involves Newton's second law, gravitational force, and the apparent weight formula. Suitable for Grades 10-12 physics students.

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