A person of mass 53.8 kg weighs 807 N on Planet A. The person's mass is now doubled. If Planet B's gravitational acceleration is 2 times the gravitational acceleration of Planet A, what is the weight of the same person on Planet B's surface correct to the nearest whole number?

Question

BlackTom AI · Accepted Answer

Weight equals mass multiplied by gravitational acceleration, W = m g. Use the given data to find g on Planet A and then apply Planet B’s gravity.

1) Relevant concepts
- Weight W = m g (force due to gravity).
- If Planet B’s gravitational acceleration is 2 times Planet A’s, g_B = 2 g_A.
- Use the original mass for the “same person” on Planet B’s surface.

2) Step-by-step reasoning and calculations
- Given: m = 53.8 kg and W_A = 807 N on Planet A.
- Compute g_A: g_A = W_A / m = 807 N / 53.8 kg = 15.0 m/s^2 (exactly, because 53.8 × 15 = 807).
- Compute g_B: g_B = 2 × g_A = 2 × 15.0 = 30.0 m/s^2.
- Use the same person’s original mass on Planet B: W_B = m × g_B = 53.8 kg × 30.0 m/s^2.
- Multiply: 53.8 × 30.0 = 1614.0 N.

3) Intermediate arithmetic shown
- 807 ÷ 53.8 = 15.0
- 2 × 15.0 = 30.0
- 53.8 × 30.0 = 1614.0

4) Why the correct answer is correct
Applying W = m g with the original mass and the doubled gravitational acceleration gives 1614 N. The calculation follows directly and exactly from the definitions and the given numerical values.

5) Why the other choices are incorrect
- (a) 404 N is half of 807 N; that would correspond to halving mass or gravity, which the problem does not state.
- (c) 3228.00 N equals 4 × 807 N; this would result if both mass and gravity were doubled and both factors were applied — not the intended interpretation for the “same person” here.
- (d) 7.17 N is orders of magnitude too small and inconsistent with the given masses and gravities.

Final confirmation: The calculated weight on Planet B is 1614.00 N, which matches choice b.

A person of mass 53.8 kg weighs 807 N on Planet A. The person's mass is now doubled. If Planet B's gravitational acceleration is 2 times the gravitational acceleration of Planet A, what is the weight of the same person on Planet B's surface correct to the nearest whole number?单项选择题

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