A woman stands on a scale in a moving elevator. Her mass is 71.0 kg, and the combined mass of the elevator and scale is an additional 815 kg. Starting from rest, the elevator accelerates upward. During the acceleration, the hoisting cable applies a force of 9440 N. What does the scale read during the acceleration?
tension= totalmass*(acceleration+ g)
solve for acceleration
now, given acceleration, scale reads mg+ma where m is the mass of the woman.
To determine what the scale reads during the acceleration, we need to calculate the net force acting on the woman and then use that to determine her weight, which is what the scale measures.
First, let's calculate the net force acting on the woman. We can do this by using Newton's second law of motion, which states that the net force (F_net) acting on an object is equal to its mass (m) multiplied by its acceleration (a):
F_net = m * a
In this case, the mass of the woman is given as 71.0 kg, and the force acting on her is the tension in the hoisting cable, which is 9440 N. Since the elevator is accelerating upward, we know the acceleration is positive. So we can rewrite the equation as:
F_net = 9440 N
m = 71.0 kg
a = ?
Now we can rearrange the equation to solve for the acceleration:
F_net = m * a
9440 N = 71.0 kg * a
a = 9440 N / 71.0 kg
Evaluating the expression, we find:
a = 132.96 m/s²
Now that we know the acceleration, we can calculate the net force acting on the woman using the equation:
F_net = m * a
F_net = 71.0 kg * 132.96 m/s²
Evaluating the expression, we find:
F_net = 9440.16 N
Since the scale measures the normal force acting on the woman, which is equal to her weight, we can conclude that the scale will read 9440.16 N, or approximately 9440 N, during the acceleration.