A 1500 kg cart moves at 15 m/s around a curve with radius 30 m. What are the centripetal acceleration and the necessary centripetal force?

A 1500 kg cart moves at 15 m/s around a curve with radius 30 m. What are the centripetal acceleration and the necessary centripetal force?

• A. a_c = 7.5 m/s^2; F_c = 11250 N
• B. a_c = 5.0 m/s^2; F_c = 7500 N
• C. a_c = 3.0 m/s^2; F_c = 4500 N
• D. a_c = 10.0 m/s^2; F_c = 15000 N

Answer: (C)

When an object moves in a circle, it experiences a centripetal acceleration directed toward the center of the circle. Its magnitude is a_c = v^2 / r, and the centripetal force is F_c = m a_c = m v^2 / r. Plug in the numbers: v = 15 m/s and r = 30 m. The centripetal acceleration is a_c = (15)^2 / 30 = 225 / 30 = 7.5 m/s^2. The required inward force is F_c = 1500 kg × 7.5 m/s^2 = 11250 N. So the correct values are a_c = 7.5 m/s^2 and F_c = 11250 N. The alternative numbers would correspond to a different radius (for example, a_c = 3.0 m/s^2 would need r = v^2 / a_c = 225 / 3 = 75 m).

When an object moves in a circle, it experiences a centripetal acceleration directed toward the center of the circle. Its magnitude is a_c = v^2 / r, and the centripetal force is F_c = m a_c = m v^2 / r.

Plug in the numbers: v = 15 m/s and r = 30 m. The centripetal acceleration is a_c = (15)^2 / 30 = 225 / 30 = 7.5 m/s^2. The required inward force is F_c = 1500 kg × 7.5 m/s^2 = 11250 N.

So the correct values are a_c = 7.5 m/s^2 and F_c = 11250 N. The alternative numbers would correspond to a different radius (for example, a_c = 3.0 m/s^2 would need r = v^2 / a_c = 225 / 3 = 75 m).