Final answer:
To find the tension in the elevator cable during upward acceleration, you calculate the mass of the elevator from its weight, then apply Newton's second law to include the force needed for the acceleration.
Step-by-step explanation:
To determine the tension in the cable when the elevator is being accelerated upward, we use Newton's second law of motion, which states that the force (F) acting on an object is equal to the mass (m) of the object times its acceleration (a): F = m * a. The overall force on the elevator not only has to support the weight of the elevator (which is the force due to gravity), but also provide enough extra force to accelerate it upward.
The elevator's weight (W) is given by W = m * g, where m is the mass of the elevator and g is the acceleration due to gravity. The tension (T) in the cable must be equal to the weight of the elevator plus the additional force required for the upward acceleration: T = W + (m * a).
First, calculate the mass (m) of the elevator by using the weight (W = 20,000 N) and the acceleration due to gravity (g = 9.80 m/s2): m = W / g. Then, find the tension (T) using the given acceleration (a = 3.00 m/s2): T = W + (m * a).