Final answer:
The tension force pulling the elevator is calculated using the mass, gravitational acceleration, and the elevator's acceleration. By applying Newton's second law, the tension is found to be 4170 N.
Step-by-step explanation:
To determine the tension force pulling an elevator that is accelerating upward, we must calculate the net force acting on the elevator and then apply Newton's second law of motion. The tension force (ℓ) in an elevator cable can be calculated using the equation:
ℓ = m(g + a)
where m is the mass of the elevator, g is the acceleration due to gravity, and a is the acceleration of the elevator.
In this scenario, the elevator has a mass (ℓ) of 300 kg, an upward acceleration (ℓ) of 3.5 m/s², and the force of gravity (ℓ) acting on it is 2940 N (300 kg × 9.8 m/s²). Using the equation, the tension can be calculated as follows:
ℓ = 300 kg (9.8 m/s² + 3.5 m/s²) = 300 kg × 13.3 m/s² = 3990 N.
However, we need to account for the force of gravity, which acts in the opposite direction to the acceleration. This gives us:
ℓ = m(g + a) = 300 kg × 9.8 m/s² + 300 kg × 3.5 m/s² = 4170 N.
Thus, the correct answer is b) 4170 N.