An elevator is moving vertically up with a acceleration a the force exerted on the floor by a passenger of mass m is

Options

A. mg
B. ma
C. mg - ma
D. mg + ma

Explanation

To solve the problem, we need to determine the force exerted on the floor of the elevator by a passenger of mass \( m \) when the elevator is moving upwards with an acceleration \( a \).

### Step-by-Step Solution:

1. **Identify the Forces Acting on the Passenger**:
- The passenger experiences two main forces:
- The gravitational force acting downwards, which is given by \( F_g = m \cdot g \), where \( g \) is the acceleration due to gravity.
- The pseudo force acting downwards due to the upward acceleration of the elevator, which is given by \( F_p = m \cdot a \).

2. **Calculate the Total Downward Force**:
- The total force acting downwards on the passenger is the sum of the gravitational force and the pseudo force:
\[ F_{\text{down}} = F_g + F_p = m \cdot g + m \cdot a = m(g + a) \]

3. **Determine the Normal Force Exerted by the Passenger**:
- According to Newton's third law, the force exerted by the passenger on the floor of the elevator (the normal force \( N \)) is equal in magnitude and opposite in direction to the total downward force acting on the passenger. Therefore:
\[ N = F_{\text{down}} = m(g + a) \]

4. **Final Expression**:
- The force exerted on the floor by the passenger is:
\[ N = m(g + a) \]

### Conclusion:
The force exerted on the floor by a passenger of mass \( m \) in an elevator moving upwards with acceleration \( a \) is given by:
\[ N = m(g + a) \]