A 64kg person is standing on a scale in an elevator. the elevator is rising at a constant velocity but then begins to slow, with an acceleration of 0.59m/s^2. What is the sign of the acceleration? What is the reading on the scale while the elevator is accelerating.
fg +fps = ma
where fg is the force due to gravity
fps is the force due to the person on the scale
ma is the submission of the forces of Fy
re-arrange the formula to find Fps.
The sign of the acceleration in this case is negative because the elevator is slowing down.
To find the reading on the scale while the elevator is accelerating, we need to consider the forces acting on the person.
When the elevator is moving at a constant velocity, the person experiences two forces: the force of gravity (mg) acting downwards and the normal force (N) exerted by the scale acting upwards. These forces balance each other out, resulting in a net force of zero and no acceleration.
However, when the elevator begins to slow down with an acceleration of -0.59 m/s^2, the net force acting on the person is no longer zero. The downward force of gravity remains the same (mg), but the normal force exerted by the scale decreases. This decrease in the normal force is what causes the person to feel lighter while the elevator is accelerating downwards.
To find the reading on the scale, we need to use Newton's second law, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration. In this case, the net force is the difference between the downward force of gravity and the upward normal force.
Net force = m * a
The downward force of gravity can be calculated as the person's mass (64 kg) multiplied by the acceleration due to gravity, g (approximately 9.8 m/s^2):
Force of gravity = m * g = 64 kg * 9.8 m/s^2 ≈ 627.2 N
The net force is then:
Net force = m * a = 64 kg * (-0.59 m/s^2) ≈ -37.76 N
Since the normal force exerted by the scale balances the downward force of gravity, the reading on the scale should be equal to the magnitude of the normal force:
Reading on the scale = |Net force| = |-37.76 N| ≈ 37.76 N
Therefore, the reading on the scale while the elevator is accelerating downwards is approximately 37.76 Newtons.
To determine the sign of acceleration, we should identify the direction in which the elevator is moving. In this scenario, the elevator is rising, which means it is moving in the positive direction. If the elevator begins to slow down, it means the acceleration is directed opposite to the direction of motion, which is downward.
Next, we need to calculate the reading on the scale while the elevator is accelerating. To do this, we need to consider the forces acting on the person in the elevator. The two main forces are gravity and the normal force exerted by the scale.
When the elevator is rising at a constant velocity, the acceleration is zero, and the net force on the person is zero. This means the normal force and the gravitational force are equal in magnitude and opposite in direction. The reading on the scale is equal to the person's weight, which is the gravitational force acting on them. In this case, the person weighs 64kg, so the reading on the scale is 64kg multiplied by the acceleration due to gravity (9.8 m/s^2).
However, when the elevator begins to slow down with an acceleration of 0.59 m/s^2, the net force on the person is no longer zero. The normal force exerted by the scale must now be greater than the gravitational force to provide an upward net force and cause the person to slow down with the elevator. Consequently, the reading on the scale will be greater than the person's weight while the elevator is accelerating.
Therefore, the sign of the acceleration is negative, indicating a downward direction, and the reading on the scale will be greater than 64kg multiplied by 9.8 m/s^2 while the elevator is accelerating.