For a vertical circle with radius 1.5 m, what is the minimum speed at the top to maintain the circular path?

For a vertical circle with radius 1.5 m, what is the minimum speed at the top to maintain the circular path?

• A. 2.5 m/s
• B. 4.5 m/s
• C. 3.83 m/s
• D. 5.0 m/s

Answer: (C)

The main idea is that to keep moving in a vertical circle, the inward (toward the center) acceleration required is the centripetal acceleration v^2/r. At the top, gravity already points toward the center, so the smallest speed that still provides the needed inward force is when the normal force from the track is zero. In that limiting case, m v^2 / r = m g, so v = sqrt(g r). With r = 1.5 m and g ≈ 9.8 m/s^2, v = sqrt(9.8 × 1.5) = sqrt(14.7) ≈ 3.83 m/s. So the minimum speed at the top is about 3.83 m/s.

The main idea is that to keep moving in a vertical circle, the inward (toward the center) acceleration required is the centripetal acceleration v^2/r. At the top, gravity already points toward the center, so the smallest speed that still provides the needed inward force is when the normal force from the track is zero. In that limiting case, m v^2 / r = m g, so v = sqrt(g r).

With r = 1.5 m and g ≈ 9.8 m/s^2, v = sqrt(9.8 × 1.5) = sqrt(14.7) ≈ 3.83 m/s. So the minimum speed at the top is about 3.83 m/s.