How Does Speed Affect Your Apparent Weight?
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: Meaning, Formula & Applications
1. What is the definition of apparent weight in physics, and how does it differ from true weight?
Apparent weight is the force an object exerts on the surface that supports it. It is the reading you would see on a weighing scale. True weight, on the other hand, is the gravitational force exerted on an object's mass (W = mg). The key difference is that apparent weight can change based on the object's acceleration or other forces acting on it, while true weight remains constant in a given gravitational field.
2. What is the formula for calculating apparent weight in different scenarios, such as in an elevator?
The apparent weight (W_app) is equal to the normal force (N) acting on the body. The formula changes depending on the acceleration (a) of the frame of reference, like an elevator:
Elevator accelerating upwards: The apparent weight increases. Formula: W_app = m(g + a).
Elevator accelerating downwards: The apparent weight decreases. Formula: W_app = m(g - a).
Elevator at rest or moving with constant velocity: The apparent weight equals the true weight. Formula: W_app = mg.
In free fall (cable snaps): The acceleration equals gravity (a = g), so the apparent weight is zero. Formula: W_app = m(g - g) = 0.
3. Why do you feel heavier when an elevator accelerates upwards and lighter when it goes down?
This feeling is a direct result of the changing normal force, which we perceive as our weight. When an elevator accelerates upwards, the floor must push on you with a force greater than your true weight to overcome your inertia and move you up. This increased normal force makes you feel heavier. Conversely, when it accelerates downwards, the floor doesn't need to support your full weight because gravity is already pulling you in that direction. The reduced normal force makes you feel lighter.
4. What are some important real-world applications and examples of apparent weight?
The concept of apparent weight is crucial in many real-world situations. Some key examples include:
Elevators: The most common example demonstrating how acceleration changes our perceived weight.
Astronauts in Orbit: They experience a state of 'weightlessness' because they are in continuous free-fall around the Earth, making their apparent weight zero.
Roller Coasters: Riders feel heavier at the bottom of a dip (upward acceleration) and almost weightless at the crest of a hill (downward acceleration).
Objects in Fluids: An object submerged in water has a lower apparent weight due to the upward buoyant force acting on it.
5. How does buoyancy affect the apparent weight of an object submerged in a fluid?
When an object is submerged in a fluid like water, it experiences an upward force called the buoyant force. According to Archimedes' principle, this force is equal to the weight of the fluid displaced by the object. This upward buoyant force counteracts the downward force of gravity, reducing the net downward force. Therefore, the apparent weight of a submerged object is its true weight minus the buoyant force (W_app = W_true - F_buoyant). This is why things feel lighter in water.
6. Is an astronaut floating in the International Space Station (ISS) truly weightless?
This is a common misconception. An astronaut in the ISS is not truly weightless, as Earth's gravity at that altitude is still about 90% as strong as it is on the surface. Their true weight is significant. However, they experience zero apparent weight because both the astronaut and the space station are in a constant state of free-fall around the Earth. Since there is no support surface pushing back on them, the normal force is zero, creating the sensation of weightlessness.
7. Under what conditions can an object’s apparent weight be zero or even negative?
An object's apparent weight can become zero or negative under specific conditions of acceleration:
Zero Apparent Weight: This occurs during free-fall, where the only force acting on the object is gravity. The downward acceleration (a) equals the acceleration due to gravity (g), resulting in W_app = m(g - g) = 0.
Negative Apparent Weight: This can happen if an object has a downward acceleration greater than g (a > g). For instance, on a roller coaster that is forcefully accelerated downwards faster than gravity, you would be lifted from your seat. The seat would need to pull you down to keep you in it, resulting in a negative normal force, which is a negative apparent weight.
