A person stands on a scale in an elevator. As the elevator starts, the scale has a constant reading of 600 N. As the elevator later stops, the scale reading is 396 N. Assume the magnitude of the acceleration is the same during starting and stopping.
A)Determine the wieght of the person.
B) Determine the mass of the person
C)Determine the magnitude of acceleration of the elevator.
scale= mg+ma when going accelerating upwards, = mg-ma when acceleration is downward (as when going up and slowing).
396=m(g)
so you can solve for mass then.
600=396+ma and you can solve for a.
A) To determine the weight of the person, we need to understand that weight is the force of gravity acting on an object. In this case, the weight of the person is equal to the reading on the scale when the elevator is at rest.
Given that the reading on the scale is 600 N when the elevator is at rest, we can conclude that the weight of the person is 600 N.
B) To determine the mass of the person, we can use the formula F = ma, where F is the force, m is the mass, and a is the acceleration. In this scenario, the force is the reading on the scale when the elevator is in motion.
When the elevator starts moving, the reading on the scale is 600 N. However, during the elevator stop, the reading on the scale is 396 N. This change in force is due to the acceleration of the elevator. Since the magnitude of acceleration is the same during starting and stopping, the difference in force is equal to the force exerted by the person's mass.
Using the formula F = ma, we can rearrange it to solve for mass: m = F/a.
The change in force is given by 600 N - 396 N = 204 N.
Now we can substitute the values into the formula: mass = 204 N / a.
C) To determine the magnitude of acceleration, we can use the difference in force and the mass of the person. Rearranging the formula F = ma, we have a = F/m.
Substituting the known values, we have: acceleration = 204 N / mass.
To find the mass from part B, substitute it into the equation to calculate the acceleration of the elevator.
A) To determine the weight of the person, we need to consider the reading on the scale when it is at rest. The scale reading when the elevator is at rest is equal to the person's weight. In this case, the reading is 600 N. Therefore, the weight of the person is 600 N.
B) To determine the mass of the person, we can use the formula: weight = mass * acceleration due to gravity. The weight, as we calculated earlier, is 600 N. The acceleration due to gravity is approximately 9.8 m/s^2. Rearranging the formula, we have: mass = weight / acceleration due to gravity. So, the mass of the person is 600 N / 9.8 m/s^2 = 61.2 kg (rounded to one decimal place).
C) To determine the magnitude of acceleration of the elevator, we can use the concept of net force. When the elevator starts, the force acting on the person is the difference between their weight and the scale reading, which is 600 N - 396 N = 204 N. This force is equal to the mass of the person multiplied by the acceleration of the elevator, as per Newton's second law, F = ma. We know the mass of the person is 61.2 kg. Therefore, rearranging the formula, we have: acceleration = force / mass = 204 N / 61.2 kg = 3.33 m/s^2 (rounded to two decimal places). Thus, the magnitude of acceleration of the elevator is 3.33 m/s^2.