A roller coaster moves on a circular portion of the track. The cart is upside down when it reaches the top portion of the track. (a) Determine how fast a roller coaster would have to move so that the acceleration at the top of the loop is 3g if r=10m (b) Determine the normal force exerted by the seat on a 45kg passenger
Added by Ver-Nica M.
Step 1
At the top of the loop, the gravitational force (weight) acts downward, and the centripetal force required to keep the roller coaster moving in a circle also acts downward. The net force at the top of the loop is the sum of these forces. Show more…
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Modern roller coasters have vertical loops like the one shown here. The radius of curvature is smaller at the top than on the sides so that the downward centripetal acceleration at the top will be greater than the acceleration due to gravity, keeping the passengers pressed firmly into their seats. (a) What is the speed of the roller coaster at the top of the loop if the radius of curvature there is $15.0 \mathrm{m}$ and the downward acceleration of the car is $1.50 \mathrm{g}$ ? (b) How high above the top of the loop must the roller coaster start from rest, assuming negligible friction? (c) If it actually starts $5.00 \mathrm{m}$ higher than your answer to (b), how much energy did it lose to friction? Its mass is $1.50 \times 10^{3} \mathrm{kg}$
Modern roller coasters have vertical loops like the one shown in the figure. The radius of curvature is smaller at the top than on the sides so that the downward centripetal acceleration at the top will be greater than the acceleration due to gravity, keeping the passengers pressed firmly into their seats. a) What is the speed of the roller coaster, in meters per second, at the top of the loop if the radius of curvature there is 12 m and the downward acceleration of the car is 1.5g? Note that g here is the acceleration due to gravity. b) The beginning of this roller coaster is at the top of a high hill. If it started from rest at the top of this hill, how high, in meters, above the top of the loop is this initial starting point? You may assume there is no friction anywhere on the track. c) If it actually starts 6.5 m higher than your answer to the previous part (yet still reaches the top of the loop with the same velocity), how much energy, in joules, did it lose to friction? Its mass is 1800 kg.
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