To solve this problem, we need to determine the tension force that is pulling the elevator upward. This tension force will be due to two components:
1. The gravitational force acting on the elevator.
2. The force needed to accelerate the elevator upward.
Here are the steps to find the solution:
1. Identify the given values:
- The acceleration [tex]\( a = 3.5 \, \text{m/s}^2 \)[/tex].
- The mass of the elevator [tex]\( m = 300 \, \text{kg} \)[/tex].
- The gravitational force [tex]\( F_g = 2,940 \, \text{N} \)[/tex].
2. Calculate the force required for the upward acceleration:
We use Newton's second law, which states that [tex]\( F = m \times a \)[/tex], where [tex]\( F \)[/tex] is the force, [tex]\( m \)[/tex] is the mass, and [tex]\( a \)[/tex] is the acceleration.
[tex]\[
F_{\text{acceleration}} = m \times a
\][/tex]
Substituting the given values:
[tex]\[
F_{\text{acceleration}} = 300 \, \text{kg} \times 3.5 \, \text{m/s}^2 = 1,050 \, \text{N}
\][/tex]
3. Determine the total tension force:
The total tension force [tex]\( F_t \)[/tex] is the sum of the gravitational force and the force required for the upward acceleration.
[tex]\[
F_t = F_g + F_{\text{acceleration}}
\][/tex]
Substituting the given gravitational force and the calculated force for acceleration:
[tex]\[
F_t = 2,940 \, \text{N} + 1,050 \, \text{N} = 3,990 \, \text{N}
\][/tex]
Therefore, the tension force pulling the elevator upward is:
[tex]\[
F_t = 3,990 \, \text{N}
\][/tex]
