e in This Example The Mo × + enext 90273900 Item 7 7ot7 > In this example the mo

Question

e in This Example The Mo × + enext 90273900 Item 7 7ot7 > In this example the motion is in a vertical circle Passengers in a carnival ride travel in a circle with radius 5.0 m The ride moves at a constant speed and makes one complete circle in a time T-4.0s What is the acceleration of the passengers? SOLUTION SET UP (Figure 1) shows our diagram. SOLVE We will use the equation a /R To find the speed v, we use the fact that a passenger travels a distance equal to the circumference of the circle (2mR) in the time T" for one revolution: U = = 2T(5 0 m) 2xR 2(5.0 ED) = 7.9 m/s The centripetal acceleration is arad,(7.9 m/s,--12 m/s2 REFLECT The direction of a is toward the center of the cirdle. The magnitude of à is greater than g, the acceleration due to gravity, so this is not a ride for the faint-hearted (But some roller coasters subject their passengers to accelerations as great as 4g)

Explanation / Answer

distance travelled in one time period, d = 2*pi*R

speed of the passenger, v = d/T

= 2*pi*R/T

= 2*pi*5/4

= 7.85 m/s

centripetal acceleration, a_centripetal = v^2/R

= 7.85^2/5

= 12.3 m/s^2

= 12 m/s^2 (when rounded to two significant figures)

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