Q#1 The purpose of a banked curve is to allow vehicles tomaneuver through the tu
ID: 1674812 • Letter: Q
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Q#1 The purpose of a banked curve is to allow vehicles tomaneuver through the turn without relying on static tire frictionto remain on the curve. An accident invest igator is trying todetermine whether or not a highway clover leaf on-ramp speed limitsign is correct for a banked curve with a 12.0 degree bankingangle. Assume the curve has a radius of 67 m. (a) what should thecautionary speed be for this curve? (b) If a 1200kg vehicleattempts to make the turn at a higher speed than the cautionaryspeed , frictional force must provide the additional centripetalforce to keep the vehicle from sliding. what is the frictionalforce necessary to keep the car from sliding assume the drivermaintain a constant velocity of 95 km/h (59mph) ? Q#1 The purpose of a banked curve is to allow vehicles tomaneuver through the turn without relying on static tire frictionto remain on the curve. An accident invest igator is trying todetermine whether or not a highway clover leaf on-ramp speed limitsign is correct for a banked curve with a 12.0 degree bankingangle. Assume the curve has a radius of 67 m. (a) what should thecautionary speed be for this curve? (b) If a 1200kg vehicleattempts to make the turn at a higher speed than the cautionaryspeed , frictional force must provide the additional centripetalforce to keep the vehicle from sliding. what is the frictionalforce necessary to keep the car from sliding assume the drivermaintain a constant velocity of 95 km/h (59mph) ?Explanation / Answer
a) to obtain a decent cautionary speed, one must ignore friction'scontribution to centripetal force. Thus the only other force to provide this force is the normalreaction component. The freebody diagram suggests the following forces: Ncos12=mg Nsin12=mv2/r ----this force provides the necessarycentripetal force. mv2/r=mgtan12(by substituting for N in equation 2) v=rgtan12 This v is the max permissible value ofvelocity.... v=67*9.8*tan12 =11.81m/s b) if v=95km/h =26.39m/s....... Ncos12=mg+Ffsin12 N=(mg+Ffsin12)/cos12 =mg/cos12+Fftan12 Ffcos12+Nsin12=mv2/r Ffcos12+(mg/cos12+Fftan12)*sin12=mv2/r Ffcos12+mgtan12+Fftan12*sin12=mv2/r Ff(cos12+tan12*sin12)=mv2/r-mgtan12 Ff=[mv2/r-mgtan12]/(cos12+tan12*sin12) =[12472.36-2499.67]/(1.022) =9754.76N
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