To determine the tension force pulling the elevator upward, we need to consider both the gravitational force acting on the elevator and the force required to accelerate it upward.
Step 1: Understanding the forces involved
1. Gravitational Force (Weight): This is the force due to gravity acting on the elevator. Given:
[tex]\[ F_g = 2940 \, \text{N} \][/tex]
2. Upward Acceleration: The elevator needs additional force to accelerate upwards at a rate of [tex]\( 3.5 \, \text{m/s}^2 \)[/tex].
3. Mass of the Elevator: The mass [tex]\( m \)[/tex] is given as [tex]\( 300 \, \text{kg} \)[/tex].
Step 2: Calculate the net force required for the upward acceleration
The net force required to accelerate the elevator upward is given by Newton's second law:
[tex]\[ F_\text{net} = m \cdot a \][/tex]
Where:
- [tex]\( m = 300 \, \text{kg} \)[/tex]
- [tex]\( a = 3.5 \, \text{m/s}^2 \)[/tex]
Substituting the given values:
[tex]\[ F_\text{net} = 300 \, \text{kg} \times 3.5 \, \text{m/s}^2 = 1050 \, \text{N} \][/tex]
Step 3: Calculate the total tension force
The tension force [tex]\( T \)[/tex] in the cable must counteract the gravitational force and provide the net force required for upward acceleration. Therefore, we sum the gravitational force and the net force:
[tex]\[ T = F_g + F_\text{net} \][/tex]
Substitute the values we have:
[tex]\[ T = 2940 \, \text{N} + 1050 \, \text{N} = 3990 \, \text{N} \][/tex]
So, the tension force pulling the elevator up is [tex]\( \boxed{3990} \, \text{N} \)[/tex].
