What Is Apparent Weight Formula Derivation and Solved Examples
Accordingly, the apparent weight of an object that is accelerating is equal to the vector sum of its true weight and the negative of all of its acceleration forces. 'M' represents mass minus mass times frame acceleration multiplied by the real weight of that mass. It is gravity that determines your true weight- it is the force exerted upon you by gravity, which is usually the earth's gravity.
Formula for Apparent Weight
The apparent weight can be calculated using the formula below. You appear to weigh more than your actual weight if you add to it the effect of your acceleration.
A weight is usually measured as the vector difference between an object's acceleration and gravity's acceleration multiplied by its mass. Appearance weight can therefore be defined as a vector with a range of movement, not only vertically.
As a result, the apparent weight formula is; a = dv/dt
Real vs Apparent Weight
Real weight = true weight, so it follows that real weight = true weight. Do you know what your real weight is? It's simply the mg. It's the mass multiplied by gravity.
The apparent weight is represented by WA. It's described as;
WA = N
As shown, 'N' represents the normal force in the direction opposite to the direction of gravity. Basically, it means the opposite of the direction of the earth's center. It is possible that someone is pushing you horizontally while you are standing. Normally, this response is not taken into account. Normal Forces are a one-dimensional force.
Consider that you have just lost your cat and you are jumping from the top of the building. You are falling and your '(True) Weight' is simply mg. You appear to weigh zero. Due to the absence of normal force currently exerted on you by the ground (assuming you finally reach it, the ground will apply normal force).
If you are at rest in an elevator, imagine you are standing there. The (‘True’) weight, of course, is mg. Nevertheless, the apparent weight is mg as well. When at rest, N = mg.
The elevator moves at a constant speed: N = mg.
Assume that the magnitude of an elevator's acceleration is: |a|.
Elevator going up and slowing down: N = mg − m|a|.
Elevator going up, and increasing speed: N = mg + m|a|.
Elevator going downwards and slowing down: N = mg + m|a|.
Elevator going up, and growing speed: N = mg − m|a|.
Changing Speed
When something is continuously pulled (with nothing dragging it back), it will speed up continuously! There is an association between force and speed.
When an elevator first begins to descend, you feel lighter, whereas when it slows down again and moves upward steadily, you feel heavier.
The reason for that is because the apparent weight must change if the speed changes!
There is no difference in apparent weight in an elevator that is moving at a constant speed in comparison with an elevator that is stationary. How can this be? An object must be moved with force in order to move more quickly or slower. The force that is applied is not increased if something moves at a constant speed.
In a moving car or train, you can sit comfortably and everything seems normal except when the driver accelerates, decelerates or puts the brakes on.
Apparent Weight in Lift
Here is how much the apparent weight of a man is in a lift or elevator.
In a lift, a young boy with a mass of 'm' stands on a weighing machine. The weight of the man will be 'mg'. As a result, the machine is burdened by this weight. The machine also expends a reactionary force ‘R’ on the boy in an upward direction where ‘R = W’ (Newton’s 3rd Law). Consequently, the boy is under the influence of both reactionary and gravitational forces. Considering the two forces are in opposing directions, the net force on the boy can be calculated as follows:
F = mg – R (downwards)
The person is at rest (no acceleration) thus, the net force on him must be zero, that is
F = mg – R = 0
R = mg
FAQs on Apparent Weight in Physics and Mathematics Explained Clearly
1. What is apparent weight in physics?
The apparent weight of an object is the force exerted by a support or scale on the object, which may differ from its actual weight due to acceleration. In simple terms, it is the reading shown on a weighing scale.
- Actual weight = mg (mass × gravitational acceleration).
- Apparent weight = Normal reaction force (N).
- If there is no acceleration, apparent weight equals actual weight.
- If the system accelerates, apparent weight changes.
2. What is the formula for apparent weight?
The formula for apparent weight depends on the direction of acceleration and is given by N = m(g ± a).
- If accelerating upward: N = m(g + a)
- If accelerating downward: N = m(g − a)
- If at rest or moving with constant velocity: N = mg
3. Why does apparent weight change in an elevator?
Apparent weight changes in an elevator because the normal force acting on a person varies when the elevator accelerates.
- When the elevator accelerates upward, the scale reading increases: N = m(g + a).
- When it accelerates downward, the scale reading decreases: N = m(g − a).
- When moving at constant speed, apparent weight equals mg.
4. What is the difference between actual weight and apparent weight?
The difference between actual weight and apparent weight is that actual weight is the gravitational force mg, while apparent weight is the normal reaction force experienced by the object.
- Actual weight = mg (constant at a given location).
- Apparent weight = N (can change with acceleration).
- They are equal only when acceleration is zero.
5. How do you calculate apparent weight in an upward accelerating lift?
To calculate apparent weight in an upward accelerating lift, use the formula N = m(g + a).
- Step 1: Identify mass (m).
- Step 2: Use g = 9.8 m/s².
- Step 3: Substitute acceleration (a).
N = 60(9.8 + 2) = 60 × 11.8 = 708 N.
The apparent weight is 708 N.
6. What happens to apparent weight during free fall?
During free fall, the apparent weight becomes zero because the normal reaction force is zero.
- In free fall, acceleration a = g downward.
- Using formula: N = m(g − g) = 0.
- The object experiences weightlessness.
7. Can apparent weight be greater than actual weight?
Yes, apparent weight can be greater than actual weight when the system accelerates upward.
- Formula: N = m(g + a).
- Since a is positive upward, N > mg.
- The scale reading increases.
8. How is apparent weight related to Newton’s second law?
Apparent weight is directly derived from Newton’s Second Law (F = ma) applied to vertical motion.
- Net force = N − mg = ma (upward positive).
- Rearranging gives N = m(g + a).
9. What is an example problem of apparent weight?
An example of apparent weight is calculating scale reading in a downward accelerating lift using N = m(g − a).
- Given: m = 50 kg, a = 3 m/s² downward.
- N = 50(9.8 − 3) = 50 × 6.8 = 340 N.
10. Does apparent weight depend on mass?
Yes, apparent weight depends directly on mass (m) as shown in the formula N = m(g ± a).
- If mass increases, apparent weight increases proportionally.
- If mass doubles, apparent weight also doubles.
- This linear relationship follows from Newton’s laws.
