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Difficulty: HardGravity and Free Fall

A spacecraft hovers above a moon with no atmosphere. An astronaut drops a 5 kg5\text{ kg} tool from rest and observes that it takes exactly 4 seconds4\text{ seconds} to fall 32 meters32\text{ meters} to the surface. Later, the astronaut drops a 10 kg10\text{ kg} piece of equipment from the exact same height. What is the weight of the 10 kg10\text{ kg} equipment on this moon, and how long will it take to reach the surface?

  1. Weight is 40 N40\text{ N}; fall time is 4 s4\text{ s}Answer
  2. B
    Weight is 10 kg10\text{ kg}; fall time is 4 s4\text{ s}
  3. C
    Weight is 100 N100\text{ N}; fall time is 4 s4\text{ s}
  4. D
    Weight is 40 N40\text{ N}; fall time is 2 s2\text{ s}

Answer

The weight of the equipment is 40 N40\text{ N}, and it will take 4 s4\text{ s} to fall.
The correct answer accurately calculates the moon's gravity as 4 m/s24\text{ m/s}^2 using the first object's fall data. It then applies this gravity to find the second object's weight (10 kg×4 m/s2=40 N10\text{ kg} \times 4\text{ m/s}^2 = 40\text{ N}) and correctly applies the principle that in a vacuum, mass does not affect fall time, resulting in the same 4 s4\text{ s} duration.

Step-by-Step Solution

1
Calculate the acceleration due to gravity on the moon using the kinematic equation d=12at2d = \frac{1}{2}at^2.
32=0.5×a×(42)→32=8a→a=4 m/s232 = 0.5 \times a \times (4^2) \rightarrow 32 = 8a \rightarrow a = 4\text{ m/s}^2.
The local acceleration must be known to determine the weight of the second object.
2
Determine the weight of the 10 kg10\text{ kg} equipment on the moon.
W=m×a=10×4=40 NW = m \times a = 10 \times 4 = 40\text{ N}.
Weight is the force of gravity exerted on a mass in a specific gravitational field.
3
Determine the fall time for the 10 kg10\text{ kg} equipment.
The fall time is 4 s4\text{ s}.
In a vacuum (no atmosphere), all objects accelerate downward at the exact same rate regardless of their mass.

Key Concept

Free fall kinematics and the distinction between mass and weight
Estimated Time:2m 0s
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Topics

Gravity and Free Fall

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