Question

An elevator accelerates downward at 2.4 m/s^2, what force does the elevator floor have on a 52kg passenger

Answer 1

To find the force exerted by the elevator floor on a 52 kg passenger when the elevator is accelerating downwards at \( 2.4 \, \text{m/s}^2 \), we can use Newton's second law of motion and consider the forces acting on the passenger.

1. **Calculate the weight of the passenger (force due to gravity)**:
\[
F_g = m \cdot g
\]
where:
- \( m = 52 \, \text{kg} \) (mass of the passenger)
- \( g = 9.8 \, \text{m/s}^2 \) (acceleration due to gravity)

\[
F_g = 52 \, \text{kg} \cdot 9.8 \, \text{m/s}^2 = 509.6 \, \text{N}
\]

2. **Calculate the net force acting on the passenger**:
Since the elevator accelerates downwards at \( 2.4 \, \text{m/s}^2 \), the net force can be calculated as:
\[
F_{\text{net}} = m \cdot a
\]
where \( a = 2.4 \, \text{m/s}^2 \).

\[
F_{\text{net}} = 52 \, \text{kg} \cdot 2.4 \, \text{m/s}^2 = 124.8 \, \text{N}
\]

3. **Determine the force exerted by the elevator floor (normal force)**:
The normal force \( F_N \) is given by:
\[
F_N = F_g - F_{\text{net}}
\]

Thus, substituting in the values:
\[
F_N = 509.6 \, \text{N} - 124.8 \, \text{N} = 384.8 \, \text{N}
\]

Therefore, the force that the elevator floor has on the 52 kg passenger is approximately **384.8 N**.