Concept explainers
(a)
To Find:The normal force.
(a)
Answer to Problem 94P
Explanation of Solution
Given Information:
Radius of the curve is
Banking angle is
Mass of car is
Speed of the car is
Formula Used:
The acceleration of the car along x- axis is the centripetal acceleration, that is,
Here,
Calculation:
The free-body diagram for the car on the curved road is as follows
In the free body diagram shown below, the normal force and the static friction force, both contribute to the centripetal force according to the situation described in this problem.
The speed of the car is
The net force on the x -axis is
Substitute
Multiply the equation
The net force on the y-axis is,
Multiply the above equation with
Add the equations
Rearrange the above equation for the normal force
Substitute
Conclusion:
The normal force exerts on the car is
(b)
To Find:The frictional force exerted by the pavement on the tires.
(b)
Answer to Problem 94P
The frictional force exerted by the pavement on the tires is
Explanation of Solution
Given Information:
Radius of the curve is
Banking angle is
Mass of car is
Speed of the car is
Formula Used:
The net force along the y-axis is
Calculation:
Rearrange the above equation:
Substitute
Conclusion:
The frictional force exerted by the pavement on the tires is
(c)
To Find:The coefficient of the static frictional force.
(c)
Answer to Problem 94P
Explanation of Solution
Given Information:
Radius of the curve is
Banking angle is
Mass of car is
Speed of the car is
Formula Used:
The equation for the frictional force is
Here,
Calculation:
Rearrange the above equation for
Substitute
Conclusion:
The coefficient of the minimum static frictional force is
Want to see more full solutions like this?
Chapter 5 Solutions
PHYSICS F/SCIEN.+ENGRS. W/SAPLING >IC<
- A bus negotiates a turn of radius 120 m while traveling at a speed of 96 km/h. If slipping just begins at this speed, what is the coefficient of static friction between the tires and the road? Find the optimum banking angle for the bus. With the answers, 0.605, and 31.2°arrow_forwardHow large must the coefficient of static friction be between the tires and the road if a car is to round a level curve of radius 115 m at a speed of 110 km/h?arrow_forwardA 3,000-kg truck leaves a freeway on a circular exit of radius 50 m at a speed of 15 m/s. What minimum coefficient of static friction between the tires and the road is required to keep the truck on the exit ramp without sliding?arrow_forward
- What is the maximum speed with which a 1200-kg car can round a turn a radius of 90.0 m on a flat road if the coefficient of friction between tires and road is 0.65? Is this result independent of the mass of the car?arrow_forwardA 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.arrow_forwardA vehicle drives around a flat circular corner with a radius of 105m. If the maximum coefficient of static friction between the wheels and pavement is 0.90, then what is the maximum speed that the car can maintain without skidding?arrow_forward
- What is the maximum speed at which a car can round a curve of 25m radius on a levelroad if the coefficient of static friction between the tires and the road is 0.8?arrow_forwardA cat dozes on a stationary merry-go-round, at a radius of 5.40 m from the center of the ride. Then the operator turns on the ride and brings it up to its proper tuning rate of one complete revolution every 6.00 s. What is the least coefficient of static friction between the cat and the merry-go-round that will allow the cat to stay in place when it is to the right of the center of the ride, without sliding? The directions of the three forces and the acceleration must be identified. Make a free-body diagram. Please use the blue vector to specify forces and the pink vector for acceleration. Assume that the center of rotation is to the left. DO NOT forget to label each vectors with none, mg, T, a, or FNarrow_forwardA curve that has a radius of 95 m95 m is banked at an angle of ?=10.8∘.θ=10.8∘. If a 1050 kg1050 kg car navigates the curve at 65 km/h65 km/h without skidding, what is the minimum coefficient of static friction ?sμs between the pavement and the tires?arrow_forward
- How large must the coefficient of static friction be between the tires and the road if a car is to round a level curve of radius 150 mm at a speed of 130 km/hkm/h ?arrow_forwardA cat dozes on a stationary merry-go-round in an amusement park, at a radius of 5.4 m from the center of the ride.Then the operator turns on the ride and brings it up to its proper turning rate of one complete rotation every 6.0 s.What is the least coefficient of static friction between the cat and the merry-go-round that will allow the cat to stay in place, without sliding (or the cat clinging with its claws)?arrow_forwardA highway curve has 200-ft radius and is designed to accommodate vehicles at a maximum speed of 100-mphwith the coefficient of friction between the tires and the road of 0.6. Determine (a) the banking angle of theroad, (b) the minimum speed that the road can accommodate and (c) the ideal speed for this road?arrow_forward
- College PhysicsPhysicsISBN:9781305952300Author:Raymond A. Serway, Chris VuillePublisher:Cengage LearningUniversity Physics (14th Edition)PhysicsISBN:9780133969290Author:Hugh D. Young, Roger A. FreedmanPublisher:PEARSONIntroduction To Quantum MechanicsPhysicsISBN:9781107189638Author:Griffiths, David J., Schroeter, Darrell F.Publisher:Cambridge University Press
- Physics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningLecture- Tutorials for Introductory AstronomyPhysicsISBN:9780321820464Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina BrissendenPublisher:Addison-WesleyCollege Physics: A Strategic Approach (4th Editio...PhysicsISBN:9780134609034Author:Randall D. Knight (Professor Emeritus), Brian Jones, Stuart FieldPublisher:PEARSON