Question

A toy car of mass 0.35 kg travels along a circular banked road, with banking angle 30°. The circle has radius 0.80 m. Sarah wants to make the car move as fast as possible, but if it goes too fast, it slips off the road. Therefore, Sarah cuts a 0.80- meter piece of string, attaches one end to the car, and attaches the other end to a nail stuck in the center of the circle. Unfortunately, the string is thin and cannot withstand a tension greater than 5.0 N. If the tension gets any bigger than that, the string breaks. Assume the road is slippery and friction is negligible. View from Above (Car traveling CCW) Rear View of Car (Car is headed into page) N a (string) (string) (string) a) Draw a FBD of the car. Include all forces that act on the car, the coordinate system you expect to use in your analysis, and the direction of acceleration. The orientation of your force vectors will be graded but not their length. b) How fast can the car travel around the road without breaking the string?

Answer 1

here f = centripetal bo the ncos@ 6 let the maximum - Velocity be v, from free body diagram- Noso=W=mg =.mg a N= All coso & F = TIN Sino IT Nsing Ly3 Ž T=F-Nsino - T=f-mgtano & t= mvh-ngtone as Tmad = S N so 5= 0-35 V2 - 0-38X9-8Xtan 300 0-80 30-4375 v² St1.98 # Vs Joventut Iv=4.0 mis