A woman stands on a scale in a moving elevator. Her mass is 65.0 kg, and the combined mass of the elevator and scale is an additional 757 kg. Starting from rest, the elevator accelerates upward. During the acceleration, the hoisting cable applies a force of 9550 N. What does the scale read (in N) during the acceleration?
=ma
first, the elevator.
F=m(g+a)
9550=(65+757)(g+a) where g=9.8N/kg
solve for acceleration a of the system.
Now, knowing a, the scale reading:
F=m(g+a)
F=65*(9.8+a)
put a in that, and f is the scale reading.
To find out what the scale reads during the acceleration, we need to consider the forces acting on the woman in the elevator.
1. Weight force (mg): The weight of the woman is given by the equation weight = mass × acceleration due to gravity. Assuming the acceleration due to gravity is 9.8 m/s², the weight force on the woman is mg = (65.0 kg)(9.8 m/s²) = 637 N.
2. Normal force (N): The normal force is the force exerted by a surface to support the weight of an object resting on it. In this case, it is the scale that exerts a normal force on the woman. The normal force is equal in magnitude and opposite in direction to the weight force. Therefore, the normal force is also 637 N.
3. Tension force (T): The tension force is the force exerted by the hoisting cable on the elevator. Its magnitude is given as 9550 N.
Since the elevator is accelerating upward, the net force acting on the woman is equal to the sum of the tension force and the normal force. Therefore, the scale reads the net force, which is 9550 N + 637 N = 10,187 N during the acceleration.
To find out what the scale reads during the acceleration, we need to consider the forces acting on the woman.
1. First, let's calculate the net force acting on the woman.
- The force exerted by the hoisting cable is 9550 N, acting in the upward direction.
- The gravitational force acting on the woman is her mass multiplied by the acceleration due to gravity (9.8 m/s^2), directed downward. The gravitational force can be calculated as follows:
Gravitational force = Mass * Acceleration due to gravity
= 65.0 kg * 9.8 m/s^2
- Since the elevator is accelerating upward, there is an additional force acting on the woman in the upward direction due to her inertia. This force can be determined by multiplying the combined mass of the elevator and scale by the acceleration of the elevator:
Inertial force = (Mass of elevator + Mass of scale) * Acceleration of elevator
= (757 kg + 65.0 kg) * acceleration of elevator
The net force acting on the woman can be calculated by subtracting the gravitational force and the inertial force from the force exerted by the hoisting cable:
Net force = Force exerted by hoisting cable - Gravitational force - Inertial force
2. Once we have the net force, we can calculate what the scale reads by considering Newton's second law of motion:
Net force = Mass * Acceleration
In this case, the mass in Newton's second law refers to the woman's mass, and the acceleration is the same as the elevator's acceleration.
By following these steps and plugging in the appropriate values, we can find what the scale reads during the acceleration.