5.9
Apparent Weight
True weight is the measure of the gravitational force acting on an object. However, if the object accelerates, its measured weight is different from i…
Consider an elevator at rest, having a box on a weighing scale. The gravitational force on the box equals the normal force exerted by the scale on the box, such that the magnitude of the net force on the box is zero. The scale reads the magnitude of the normal force, which is the true weight of the box.
If the elevator moves upward with a constant acceleration, the net magnitude of the force on the box equals the difference between the normal force and the gravitational force on it. The scale reads the apparent weight higher than the true weight of the box.
When the elevator accelerates downward, conventionally, the acceleration becomes negative. The apparent weight is now lower than the true weight of the box.
Now, if the elevator's cable breaks, the box with the scale will momentarily hover but eventually accelerate downward due to gravity, experiencing a free fall.
The scale reads zero, and the box appears weightless. This phenomenon is termed apparent weightlessness.
Q1: What is the difference between true weight and apparent weight?
True weight is the gravitational force acting on an object, measured when the object is at rest. Apparent weight is the normal force the scale reads, which changes when the object accelerates. In an accelerating elevator, apparent weight differs from true weight because the net force on the object is no longer zero.
Q2: Why does a scale reading increase when an elevator accelerates upward?
When an elevator accelerates upward, the normal force from the scale must overcome both the gravitational force and provide the net upward force for acceleration. The scale reads this increased normal force as apparent weight, which is greater than the true weight of the object.
Q3: What happens to apparent weight during downward elevator acceleration?
During downward acceleration, the normal force decreases because it only needs to partially support the object against gravity. The scale reads a lower apparent weight than the true weight. The net force on the object becomes negative, pointing downward as the elevator decelerates.
Q4: Why does an object appear weightless during free fall?
During free fall, both the object and the scale accelerate downward at gravitational acceleration. The normal force becomes zero because no support is needed. The scale reads zero, and the object experiences apparent weightlessness, even though gravitational force still acts on it.
Q5: How does Newton's third law relate to the normal force on a scale?
According to newton's third law introduction, the force the object exerts downward on the scale equals the normal force the scale exerts upward on the object. At rest, these forces are equal in magnitude and opposite in direction, so the scale reading equals the true weight.
Q6: Is the weightlessness experienced by astronauts in orbit the same as free fall weightlessness?
Yes, both involve apparent weightlessness. Astronauts in orbit and objects in a free-falling elevator experience the same phenomenon: they and their surroundings accelerate together under gravity. Although gravitational force acts on them, they feel weightless because they are in continuous free fall.
Q7: How does buoyant force affect apparent weight in water?
An object's apparent weight in water equals the difference between its true weight and the buoyant force acting upward. The buoyant force reduces the net downward force, making the object appear lighter than its true weight, similar to how downward acceleration reduces apparent weight.