How To Find Apparent Weight

How to Find Apparent Weight: Understanding the Forces at Play

Apparent weight is a concept that often trips up students learning physics, yet understanding it is key to grasping fundamental principles of forces and motion. This comprehensive guide will explore what apparent weight is, how it differs from true weight, and most importantly, how to find it in various scenarios, from simple stationary objects to those experiencing acceleration. We will delve into the underlying physics, providing clear explanations and practical examples to solidify your understanding. By the end, you'll be confident in calculating apparent weight in different situations.

What is Apparent Weight?

Your true weight is the force of gravity acting on your mass (W = mg, where 'm' is mass and 'g' is acceleration due to gravity). This is a constant value, determined by your mass and the gravitational field strength. However, your apparent weight is the force you feel, which can differ from your true weight depending on the forces acting upon you. It's the reading you'd get on a scale.

Think about riding in an elevator. When the elevator accelerates upwards, you feel heavier. When it accelerates downwards, you feel lighter. This change in the sensation of weight is because your apparent weight is changing, while your true weight remains constant.

Factors Affecting Apparent Weight

Several factors contribute to the difference between true weight and apparent weight:

• Acceleration: This is the most significant factor. When you accelerate upwards, the supporting force (from the ground, a scale, etc.) needs to be greater than your true weight to provide the upward acceleration. Conversely, when accelerating downwards, the supporting force is less than your true weight.
• Buoyancy: Objects submerged in fluids (liquids or gases) experience an upward buoyant force. This force reduces the apparent weight of the object. The apparent weight is the difference between the true weight and the buoyant force.
• Friction: While less significant than acceleration and buoyancy, friction can slightly affect apparent weight, especially in scenarios involving surfaces with significant friction. However, its effect is often negligible compared to the other forces involved.

How to Find Apparent Weight: Methods and Examples

Let's explore different methods to determine apparent weight in various scenarios. We'll utilize Newton's second law (F = ma, where 'F' is net force, 'm' is mass, and 'a' is acceleration) as the fundamental principle.

1. Apparent Weight in a Stationary Situation:

In a stationary situation (no acceleration), the apparent weight is equal to the true weight.

• Example: A person with a mass of 70 kg stands on a scale. The apparent weight is 70 kg * 9.8 m/s² = 686 N (approximately). The scale will read 686 N or approximately 70 kg (since the scale is calibrated to show mass).

2. Apparent Weight During Vertical Acceleration:

This is where things get interesting. We need to consider the direction of acceleration.

• Upward Acceleration: When accelerating upwards, the net force must be upwards. Therefore: Apparent Weight (W_app) = True Weight (W) + ma.

• Downward Acceleration: When accelerating downwards, the net force is downwards (though the direction of the apparent weight is still upwards). Therefore: Apparent Weight (W_app) = True Weight (W) - ma.

• Free Fall (a = g): In free fall, the acceleration is equal to the acceleration due to gravity (a = g). In this case, the apparent weight is zero (W_app = W - mg = 0). This is why astronauts feel weightless in space.

• Example (Upward Acceleration): A 70 kg person is in an elevator accelerating upwards at 2 m/s². The apparent weight is: W_app = (70 kg * 9.8 m/s²) + (70 kg * 2 m/s²) = 826 N. The person feels heavier.

• Example (Downward Acceleration): The same 70 kg person is now in an elevator accelerating downwards at 2 m/s². The apparent weight is: W_app = (70 kg * 9.8 m/s²) - (70 kg * 2 m/s²) = 546 N. The person feels lighter.

3. Apparent Weight in a Rotating System:

In a rotating system, like a Ferris wheel, the apparent weight is affected by the centripetal force. The centripetal force is directed towards the center of rotation.

• Top of the Ferris Wheel: At the top, the apparent weight is reduced because the centripetal force acts downwards, opposing the true weight. W_app = W - mv²/r (where 'v' is the tangential velocity and 'r' is the radius of the Ferris wheel).

• Bottom of the Ferris Wheel: At the bottom, the apparent weight is increased because the centripetal force acts upwards, adding to the true weight. W_app = W + mv²/r

• Example: Consider a Ferris wheel with a radius of 10 meters and a tangential velocity of 5 m/s. A 70 kg person at the bottom would experience: W_app = (70 kg * 9.8 m/s²) + (70 kg * (5 m/s)² / 10 m) = 786 N. At the top, they would feel lighter.

4. Apparent Weight in Fluids (Buoyancy):

Archimedes' principle states that an object submerged in a fluid experiences an upward buoyant force equal to the weight of the fluid displaced.

• Apparent Weight in a Fluid: W_app = W - F_B (where F_B is the buoyant force).

• Example: A block of wood with a true weight of 10 N is submerged in water. The buoyant force is 5 N. The apparent weight of the wood in water is 10 N - 5 N = 5 N.

5. Solving Problems Involving Apparent Weight:

To solve problems, follow these steps:

1. Draw a Free Body Diagram (FBD): Represent the object and all the forces acting on it (gravity, normal force, tension, etc.).
2. Choose a Coordinate System: Select a positive direction (usually upwards).
3. Apply Newton's Second Law: ΣF = ma. Resolve the forces along the chosen axes.
4. Solve for the Unknown: Solve the equation for the apparent weight (which is often represented by the normal force).

Frequently Asked Questions (FAQ)

• Q: Can apparent weight be negative? A: Yes, in certain situations like when accelerating downwards at a rate greater than 'g', the apparent weight can be negative. This means that the supporting force is in the opposite direction of gravity.

• Q: Does apparent weight change with altitude? A: Yes, slightly. As altitude increases, the acceleration due to gravity ('g') decreases, thus reducing the true weight and consequently the apparent weight. The effect is typically negligible unless at very high altitudes.

• Q: How is apparent weight measured? A: It's typically measured using a scale, which measures the normal force acting on an object.

• Q: Is apparent weight a vector or scalar quantity? A: Apparent weight is a vector quantity, having both magnitude and direction. It's usually directed upwards (opposite to the direction of gravity).

• Q: How does apparent weight relate to weightlessness? A: Weightlessness is experienced when the apparent weight is zero. This happens when the acceleration of the object matches the acceleration due to gravity.

Conclusion

Understanding apparent weight requires a firm grasp of Newton's laws of motion and the various forces acting on an object. By systematically analyzing forces and applying Newton's second law, you can successfully calculate apparent weight in diverse situations, from simple stationary scenarios to those involving complex accelerations and buoyancy. Remember to always draw a free body diagram and carefully consider the direction of all forces involved. Mastering this concept is crucial for further exploration of advanced physics topics. Through practice and a clear understanding of the underlying principles, you will confidently tackle any problem involving the calculation of apparent weight.