A person is standing on a spring bathroom
scale on the floor of an elevator which is
moving up and slowing down at the rate of
1.53 m/s
2
.
The acceleration of gravity is 9.8 m/s
2
.
If the person’s mass is 83.4 kg, what does
the scale read?
To determine what the scale reads, we need to consider the forces acting on the person while in the elevator. Let's break it down step-by-step:
Step 1: Calculate the weight of the person.
The weight of the person can be calculated using the formula: weight = mass x acceleration due to gravity.
Given that the mass of the person is 83.4 kg and the acceleration due to gravity is 9.8 m/s^2, we can calculate the weight as:
Weight = 83.4 kg x 9.8 m/s^2 = 816.12 N.
Step 2: Calculate the net force acting on the person.
The net force on the person inside the elevator is the difference between the gravitational force and the force exerted by the scale. Since the elevator is moving upward and slowing down, the net force will be upward.
Net Force = Force exerted by the scale - Weight.
Step 3: Determine the acceleration of the person.
The acceleration experienced by the person inside the elevator is given as -1.53 m/s^2 (negative because the elevator is slowing down).
Using Newton's second law, we know the net force equals mass times acceleration.
Net Force = mass x acceleration.
Therefore, Net Force = 83.4 kg x (-1.53 m/s^2) = -127.5022 N.
Step 4: Calculate the force exerted by the scale.
Now, using the calculated net force, we can find the force exerted by the scale.
Force exerted by the scale = Weight - Net Force.
Force exerted by the scale = 816.12 N - (-127.5022 N) = 943.6222 N.
Step 5: Convert the force exerted by the scale to the scale reading.
Since the scale directly measures force, the scale reading will be equal to the force exerted by the scale.
Therefore, the scale will read 943.6222 N.
To find out what the scale reads, we need to consider the forces acting on the person while they are standing on the scale. In this case, there are two main forces to consider: the force due to gravity and the normal force exerted by the scale.
1) Force due to gravity (weight):
The weight of the person can be calculated using the formula: weight = mass × acceleration due to gravity. Given that the mass of the person is 83.4 kg and the acceleration due to gravity is 9.8 m/s^2, we can calculate the weight of the person as follows:
weight = 83.4 kg × 9.8 m/s^2 = 816.12 N
2) Normal force exerted by the scale:
The normal force is the force exerted by a surface to support the weight of an object resting on it. In this case, the normal force is exerted by the scale to support the person. The normal force is equal in magnitude but opposite in direction to the force due to gravity. Therefore, the normal force can also be calculated as 816.12 N.
So, the scale would read 816.12 N.