A car of mass M = 1300 kg traveling at 45.0 km/hour enters a banked turn covered with ice. The road is banked at an angle θ, and there is no friction between the road and the car's tires. Use g = 9.80 m/s2 throughout this problem. What is the radius r of the turn if θ = 20.0 ∘ (assuming the car continues in uniform circular motion around the turn)?

A car of mass M = 1300 kg traveling at 45.0 km/hour enters a banked turn covered with ice. The road is banked at an angle θ, and there is no friction between the road and the car's tires. Use g = 9.80 m/s2 throughout this problem. What is the radius r of the turn if θ = 20.0 ∘ (assuming the car continues in uniform circular motion around the turn)?

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter5: More Applications Of Newton’s Laws

Section: Chapter Questions

Problem 59P: A single bead can slide with negligible friction on a stiff wire that has been bent into a circular...

See similar textbooks

Similar questions

A turn has a radius of R and is banked at an angle theta so that on a perfectly icy (frictionless) day a car with a speed v will not slip. What is v in terms of R and theta?
A 2000 kg car rounds a circular turn of radius 24 m. If the road is flat and the coefficient of friction between tires and road is 0.61, how fast can the car go without skidding? (Answer in m/s)
A small object with mass of 0.5kg is attached to the lower end of a long string and moves in a horizontal circle of radius 0.7 m with a constant speed of 3 m/s. What angle does the string make with the vertical?
A 50.0-kg child stands at the rim of a merry-go-round of radius 2.95 m, rotating with an angular speed of 4.00 rad/s. (a) What is the child's centripetal acceleration? (b) What is the minimum force between her feet and the floor of the carousel that is required to keep her in the circular path?(c) What minimum coefficient of static friction is required?Is the answer you found reasonable? In other words, is she likely to stay on the merry-go-round? Yes/No
A velodrome has an aggressively banked curve, where the surface makes an angle of 58.9 degrees with the horizontal. If you are biking around this curve (such that your path traces a horizontal circle with radius 21.7 m as you go around the turn), and the coefficient of static friction of your bike tires with the velodrome surface is 0.617, what is the minimum speed that you can go before starting to slip down the ramp? Give your answer in km/hr.
A 50.0-kg child stands at the rim of a merry-go-round of radius 2.00 m, rotating with an angular speed of 3.00 rad/s. (a) What is the child’s centripetal acceleration? (b) What is the minimum force between her feet and the floor of the carousel that is required to keep her in the circular path? (c) What minimum coefficient of static friction is required? Is the answer you found reasonable? In other words, is she likely to stay on the merry-go-round?
A 50.0-kg child stands at the rim of a merry-go-round of radius 2.85 m, rotating with an angular speed of 3.25 rad/s. (a) What is the child's centripetal acceleration? m/s2(b) What is the minimum force between her feet and the floor of the carousel that is required to keep her in the circular path? (c) What minimum coefficient of static friction is required?Is the answer you found reasonable? In other words, is she likely to stay on the merry-go-round? Yes No
A 50.0-kg child stands at the rim of a merry-go-round of radius 2.90 m, rotating with an angular speed of 3.65 rad/s. (a) What is the child's centripetal acceleration? m/s2(b) What is the minimum force between her feet and the floor of the carousel that is required to keep her in the circular path? N(c) What minimum coefficient of static friction is required?Is the answer you found reasonable? In other words, is she likely to stay on the merry-go-round?
A 50.0-kg child stands at the rim of a merry-go-round of radius 2.95 m, rotating with an angular speed of 3.85 rad/s. (a) What is the child's centripetal acceleration? ___________m/s2(b) What is the minimum force between her feet and the floor of the carousel that is required to keep her in the circular path? ___________N(c) What minimum coefficient of static friction is required?Is the answer you found reasonable? In other words, is she likely to stay on the merry-go-round? _____Yes _____No
A race car travels 76 m/s around a circulartrack of radius 159 m What is the magnitude of the resultantforce on the 1600 kg driver and his car ifthe car does not slip?Answer in units of kN.
A body of mass 8 kg moves in the xy-plane in a counterclockwise circular path of radius 3 meters centered at the origin, making one revolution every 10 seconds. At the time t=0, the body is at the rightmost point of the circle.A. Compute the centripetal force acting on the body at time t.⟨, ⟩B. Compute the magnitude of that force. HINT. Start with finding the angular velocity w [rad/s] of the body (the rate of change of its polar angle w.r.t. the center of rotation).Then find the position vector r→(t) of the body at time t.Then find its acceleration vector a→(t) at time t.Then use Newton's 2nd law to find the centripetal force F→(t).
A 50.0-kg child stands at the rim of a merry-go-round of radius 2.85 m, rotating with an angular speed of 3.90 rad/s. (a) What is the child's centripetal acceleration?___m/s2(b) What is the minimum force between her feet and the floor of the carousel that is required to keep her in the circular path?___N(c) What minimum coefficient of static friction is required?Is the answer you found reasonable? In other words, is she likely to stay on the merry-go-round? Yes or No ____minimum