The documentation for your slot-car set (hey that was a fun toy when I was a kid) says that the maximum centripetal acceleration the cars can withstand without being ejected from the track is 3.80 msec-2. You notice that the slot cars fly off the track if they exceed a velocity of 1.10 m sec-1 . What is the radius in meters of the curve in the track?

Question

The documentation for your slot-car set (hey that was a fun toy when I was a kid)  says that the maximum centripetal acceleration the cars can withstand without being ejected from the track is 3.80 msec-2. You notice that the slot cars fly off the track if they exceed a velocity of 1.10 m sec-1 . What is the radius in meters of the curve in the track?

BlackTom AI · Accepted Answer

The problem relates centripetal acceleration to velocity and radius via the formula a_c = v^2 / r. To find the radius r, rearrange this as r = v^2 / a_c.

Plug in the given values: v = 1.10 m/s and a_c = 3.80 m/s^2.
v^2 = (1.10 m/s)^2 = 1.21 (m^2/s^2).

Therefore r = 1.21 / 3.80 ≈ 0.318 m.

Rounding to appropriate significant figures based on the input data, the radius is about 0.318 meters. This means the curve must have a radius on the order of a few tenths of a meter to keep the centripetal acceleration beneath the 3.80 m/s^2 threshold at 1.10 m/s velocity.

EAS1600 Pressure_wind_inclass_2025

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