To solve the problem, we need to find the normal reaction exerted by the man on the floor of the elevator. Here’s the step-by-step solution:
### Step 1: Identify the forces acting on the man
When the elevator is moving upwards with an acceleration, two main forces act on the man:
1. The weight of the man (downwards), which is given by \( W = mg \), where \( m \) is the mass of the man and \( g \) is the acceleration due to gravity.
2. The normal force (upwards), which we will denote as \( N \).
### Step 2: Write down the expressions for the forces
- The weight of the man can be calculated as:
\[
W = mg
\]
Given that \( m = 50 \, \text{kg} \) and \( g \approx 9.8 \, \text{m/s}^2 \):
\[
W = 50 \times 9.8 = 490 \, \text{N}
\]
### Step 3: Apply Newton's second law
Since the elevator is accelerating upwards, we can apply Newton's second law in the vertical direction:
\[
N - W = ma
\]
Where:
- \( N \) is the normal force,
- \( W \) is the weight,
- \( m \) is the mass of the man,
- \( a \) is the acceleration of the elevator.
### Step 4: Substitute the known values into the equation
We know:
- \( W = 490 \, \text{N} \)
- \( m = 50 \, \text{kg} \)
- \( a = 0.49 \, \text{m/s}^2 \)
Substituting these values into the equation:
\[
N - 490 = 50 \times 0.49
\]
Calculating the right-hand side:
\[
50 \times 0.49 = 24.5 \, \text{N}
\]
So the equation becomes:
\[
N - 490 = 24.5
\]
### Step 5: Solve for the normal force \( N \)
Now, we can solve for \( N \):
\[
N = 490 + 24.5 = 514.5 \, \text{N}
\]
### Conclusion
The normal reaction exerted by the man on the floor of the elevator is \( 514.5 \, \text{N} \).
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