A 60 kg person stands on a scale in an elevator accelerating upward at 2.0 m/s^2. What does the scale read?

A 60 kg person stands on a scale in an elevator accelerating upward at 2.0 m/s^2. What does the scale read?

• A. About 0.6 N
• B. About 60 N
• C. About 628 N
• D. About 708 N

Answer: (D)

The scale reading is the normal force the floor exerts on you. When the elevator accelerates upward, you must be accelerated upward in addition to supporting your weight, so the floor pushes up harder. For forces along the vertical: N - m g = m a, so N = m(g + a). With m = 60 kg, g ≈ 9.8 m/s^2, and a = 2.0 m/s^2 upward, N ≈ 60 × (9.8 + 2.0) = 60 × 11.8 ≈ 708 N. So the scale reads about 708 N. If the elevator weren’t accelerating, it would read about 588 N (m g). The other numbers don’t fit the upward-acceleration situation.

The scale reading is the normal force the floor exerts on you. When the elevator accelerates upward, you must be accelerated upward in addition to supporting your weight, so the floor pushes up harder.

For forces along the vertical: N - m g = m a, so N = m(g + a). With m = 60 kg, g ≈ 9.8 m/s^2, and a = 2.0 m/s^2 upward, N ≈ 60 × (9.8 + 2.0) = 60 × 11.8 ≈ 708 N.

So the scale reads about 708 N. If the elevator weren’t accelerating, it would read about 588 N (m g). The other numbers don’t fit the upward-acceleration situation.