— ## What is True Weight? Your true weight is simply the force of gravity acting on your mass. It’s the force with which Earth pulls you downwards. * Formula: $W = mg$ * $W$: Weight (in Newtons, N) * $m$: Mass (in kilograms, kg) * $g$: Acceleration due to gravity (approximately $9.8 \text{ m/s}^2$ near Earth’s surface) Your true weight is generally constant as long as your mass doesn’t change and you stay at the same distance from the center of the Earth. — ## What is Apparent Weight? Your apparent weight is the normal force exerted on you by the surface you are standing on (like a scale, or the floor of an elevator). It’s what you feel as your weight. * Why it’s different: Apparent weight can differ from true weight when you are in a non-inertial (accelerating) reference frame. This is because the normal force must not only counteract gravity but also provide the force needed to accelerate you. * What a scale reads: A bathroom scale measures the normal force it exerts on you, which is your apparent weight. — ## Interactive: Elevator Ride Step into the elevator and observe how your apparent weight changes with different accelerations! <div class="animator-container"> <div class="input-controls"> </div> <div style="margin-bottom: 0.8rem;"> </div> Weight and Apparent Weight Elevator Simulator A simulation showing a person on a scale in an elevator, demonstrating how apparent weight changes with acceleration. Elevator True Weight: 0.0 N Apparent Weight: 0.0 N Acceleration: 0.0 m/s² <div id="animationExplanation" class="animation-explanation" aria-live="polite"> <p>Adjust your mass, then click an elevator scenario to see how your apparent weight changes!

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Scenarios for Apparent Weight

Let’s apply Newton’s Second Law ($\Sigma F = ma$) to understand apparent weight:

  • Forces:
    • $F_N$: Normal force (upwards, this is your apparent weight)
    • $W$: True weight ($mg$, downwards)
  • Equation: $\Sigma F_y = F_N - W = ma_y$
    • So, $F_N = W + ma_y$
  1. Elevator at Rest or Constant Velocity ($a_y = 0$):
    • $F_N = W + m(0) \implies F_N = W$
    • Apparent Weight = True Weight. You feel normal.
  2. Elevator Accelerating Upwards ($a_y > 0$):
    • $F_N = W + ma_y$
    • Since $ma_y$ is positive, $F_N > W$.
    • Apparent Weight > True Weight. You feel heavier.
  3. Elevator Accelerating Downwards ($a_y < 0$):
    • $F_N = W + ma_y$ (where $a_y$ is negative)
    • Since $ma_y$ is negative, $F_N < W$.
    • Apparent Weight < True Weight. You feel lighter.
  4. Elevator in Free Fall ($a_y = -g$):
    • $F_N = W + m(-g) = mg - mg \implies F_N = 0$
    • Apparent Weight = 0. You feel weightless. This is because the floor is accelerating downwards with you, so it doesn’t need to push up on you.

Why Weight and Apparent Weight Matter

  • Understanding “Weightlessness”: It explains why astronauts in orbit feel weightless (they are in continuous free fall around Earth), even though Earth’s gravity is still acting on them.
  • Roller Coasters: The “pit of your stomach” feeling on a roller coaster is due to changes in apparent weight.
  • Conceptual Clarity: It helps distinguish between the fundamental force of gravity and the sensation of weight, which is a contact force.

Audio Explanation

Prefer to listen? Here's a quick audio summary of weight and apparent weight.

💡 Quick Concept Check:

An astronaut is in orbit around Earth. Does the astronaut have true weight? Do they have apparent weight? Explain.

Click to Reveal Answer
Yes, the astronaut still has **true weight** because Earth's gravity is still pulling on them (though slightly less than on the surface). However, they have **zero apparent weight** because they are in a continuous state of free fall around the Earth, meaning there is no normal (support) force acting on them.

Ready to put your understanding of weight and apparent weight into practice? Check out these related skills:

Practice Problems

Test your understanding and apply what you've learned with these problems.

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