$$  $$An elevator accelerates upward at 1.2 m/s 2 . The acceleration of gravity is 9.8 m/s 2 . What is the upward force exerted by the floor of the elevator on a(n) 99 kg passenger? Answer in units of N.

We can calculate the upward force exerted by the floor of the elevator on the passenger using Newton's Second Law:

### Step 1: Identify the forces acting on the passenger
The forces acting on the passenger are:
1. **Weight** of the passenger, $ W = mg $, where:
   - $ m = 99 \, \text{kg} $ is the mass of the passenger,
   - $ g = 9.8 \, \text{m/s}^2 $ is the acceleration due to gravity.
2. **Normal force** exerted by the floor of the elevator, $ F_N $, which we need to find.

The elevator is accelerating upward, so the net force on the passenger is a combination of gravity and the upward acceleration due to the elevator.

### Step 2: Calculate the passenger's weight
\[
W = mg = 99 \times 9.8 = 970.2 \, \text{N}
\]

### Step 3: Use Newton's Second Law
Newton's second law states that the net force $ F_{\text{net}} $ is the mass times the acceleration:
\[
F_{\text{net}} = m a_{\text{total}}
\]
Where:
- $ m = 99 \, \text{kg} $ is the mass of the passenger,
- $ a_{\text{total}} = g + a_{\text{elevator}} $ is the total acceleration (since both the gravitational force and the elevator's upward acceleration contribute).

So, the total acceleration is:
\[
a_{\text{total}} = 9.8 + 1.2 = 11 \, \text{m/s}^2
\]

### Step 4: Calculate the net force
\[
F_{\text{net}} = m a_{\text{total}} = 99 \times 11 = 1089 \, \text{N}
\]

### Conclusion:
The upward force exerted by the floor of the elevator on the passenger is $ 1089 \, \text{N} $.

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Would you like more details or have any questions on this? Here are some follow-up questions:

1. How does the elevator's acceleration affect the force felt by the passenger?
2. What would the force be if the elevator were accelerating downward instead of upward?
3. How does the normal force change if the elevator moves at a constant velocity?
4. What would the force be if the elevator was in free fall?
5. How do you calculate the net force if the elevator were stationary?

**Tip:** Always remember to account for all the accelerations involved when calculating net forces!

An elevator accelerates upward at 1.2 m/s². The acceleration of gravity is 9.8 m/s². What is the upward force exerted by the floor of the elevator on a 99 kg passenger? Answer in units of N.

Discover how to calculate the upward force exerted on a 99 kg passenger in an elevator accelerating upward at 1.2 m/s². This solution uses Newton's Second Law, gravity (9.8 m/s²), and key force formulas. Suitable for Grades 9-12 physics students.

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