A 55 kg person stands on a scale in an elevator that accelerates downward at 3 m/s2.
a) What is the scale reading?
N
b) What is the person's weight?
N
a. F= ma = 55 * 3 = 165 N.
b. a + g = -3 m/s^2,
a - 9.8 = -3,
a = -3 + 9.8 = 6.8 m/s^2.
F = ma = 55 kg * 6.8 m/s^2 = 374 N =
The person's wt.
To answer these questions, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration.
a) What is the scale reading?
The scale reading will be equal to the normal force experienced by the person standing on the scale. In this case, the normal force is equal to the person's weight plus the force due to acceleration.
The weight of the person can be calculated using the formula: Weight = mass * acceleration due to gravity.
The acceleration due to gravity is approximately 9.8 m/s^2.
Weight = (mass of the person) * (acceleration due to gravity)
Weight = 55 kg * 9.8 m/s^2
Weight ≈ 539 N
Since the elevator is accelerating downward at 3 m/s^2, the person experiences an additional downward force due to this acceleration.
The force due to acceleration = mass of the person * acceleration of the elevator
Force due to acceleration = 55 kg * 3 m/s^2
Force due to acceleration = 165 N
Therefore, the scale reading will be:
Scale Reading = Weight + Force due to acceleration
Scale Reading = 539 N + 165 N
Scale Reading ≈ 704 N
b) What is the person's weight?
The person's weight is calculated using the formula: Weight = mass * acceleration due to gravity.
Weight = 55 kg * 9.8 m/s^2
Weight ≈ 539 N
Therefore, the person's weight in this situation is approximately 539 Newtons.
To find the scale reading and the person's weight in this scenario, we need to consider the forces acting on the person.
a) To find the scale reading, we need to calculate the apparent weight of the person. The apparent weight is the force experienced by an object in an accelerating frame of reference (in this case, the elevator).
The force acting on the person is given by the formula F = m * a, where m is the mass of the person and a is the acceleration. In this case, the mass of the person is 55 kg and the acceleration is 3 m/s^2 (accelerating downward).
So, the force acting on the person (and consequently the scale reading) can be calculated as follows:
F = 55 kg * 3 m/s^2 = 165 N
Therefore, the scale reading would be 165 N.
b) To find the person's weight, we need to consider the force due to gravity acting on the person. The weight of an object is given by the formula W = m * g, where m is the mass of the object and g is the acceleration due to gravity. In this case, the mass of the person is still 55 kg, and the acceleration due to gravity is approximately 9.8 m/s^2.
So, the weight of the person can be calculated as follows:
W = 55 kg * 9.8 m/s^2 = 539 N
Therefore, the person's weight would be 539 N.
Note: The scale reading and the person's weight are different because the scale measures the force that is exerted on it by the person (apparent weight) in the accelerating frame of reference, while the weight is the force of gravity acting on the person.