A person stands in an elevator (lift). The total mass of the person and the elevator is 800 kg.The elevator accelerates upward at 2.0 m s-2

Sure, I will solve the problem step by step.

1. Identify the forces acting on the system:

   • The gravitational force (weight) acting downward.
   • The normal force (reaction force) exerted by the elevator floor acting upward.

2. Calculate the gravitational force: The gravitational force can be calculated using the formula: $F_{\text{gravity}} = m \cdot g$ where:

   • $m$ is the mass (800 kg)
   • $g$ is the acceleration due to gravity (approximately $9.8 \, \text{m/s}^2$)

   $F_{\text{gravity}} = 800 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 7840 \, \text{N}$

3. Calculate the net force required for the upward acceleration: The net force can be calculated using Newton's second law: $F_{\text{net}} = m \cdot a$ where:

   • $a$ is the acceleration (2.0 m/s²)

   $F_{\text{net}} = 800 \, \text{kg} \times 2.0 \, \text{m/s}^2 = 1600 \, \text{N}$

4. Determine the normal force: The normal force $F_{\text{normal}}$ is the force exerted by the elevator floor to support the person and the elevator, and it must overcome both the gravitational force and provide the net upward force. Therefore: $F_{\text{normal}} = F_{\text{gravity}} + F_{\text{net}}$

   $F_{\text{normal}} = 7840 \, \text{N} + 1600 \, \text{N} = 9440 \, \text{N}$

So, the normal force exerted by the elevator floor is $9440 \, \text{N}$.