Concept explainers
A curve in a speed track has a radius of 1000 ft and a rated speed of 120 mi/h. (See Sample Prob. 12.7 for the definition of rated speed.) Knowing that a racing car starts skidding on the curve when traveling at a speed of 180 mi/h, determine (a) the banking angle θ, (b) the coefficient of static friction between the tires and the track under the prevailing conditions, (c) the minimum speed at which the same car could negotiate the curve.
Fig. P12.52
(a)
Find the banking angle
Answer to Problem 12.52P
The banking angle
Explanation of Solution
Given information:
The radius
The rated speed
The frictional force
The speed (v) at prevailing condition is 180 mi/h.
Calculation:
Write the general equation weight (W).
Here, m is the mass and g is the acceleration due to gravity.
Write the general equation of acceleration (a) in curved path.
Here, v is the speed and
Sketch the free body diagram and kinetic diagram of the racing car as shown in Figure (1).
Refer Figure (1):
Consider the racing car moves at rated speed.
Find the banking angle
Apply Newton’s law of equation along x-axis.
Substitute 0 for
Substitute 120 mi/h for
Thus, the banking angle
(b)
Find the coefficient of static friction between the tires and the track under the prevailing conditions.
Answer to Problem 12.52P
The coefficient of static friction between the tires and the track under the prevailing conditions is
Explanation of Solution
Calculation:
Refer Figure (1):
Consider the racing car moves in prevailing condition.
Apply Newton’s law of equation along y-axis.
Substitute
Apply Newton’s law of equation along y-axis.
Substitute
Find the coefficient of static friction
Write the general equation of normal force(N).
Substitute Equation (1) and (2) in Equation (3).
Substitute 180 mi/h for v,
Thus, the coefficient of static friction between the tires and the track under the prevailing conditions is
(c)
Find the minimum speed at which the same car could negotiate that curve.
Answer to Problem 12.52P
The minimum speed at which the same car could negotiate that curve is
Explanation of Solution
Calculation:
Write the general equation of normal force (N) in minimum speed.
Substitute Equation (1) and (2) in Equation (3).
Substitute 0.390 for
Thus, the minimum speed at which the same car could negotiate that curve is
Want to see more full solutions like this?
Chapter 12 Solutions
Vector Mechanics for Engineers: Statics and Dynamics
- NEED WITHIN 1HR PLEASE, THANKS 2. A truck is traveling on a level road at a speed of 90 km/h when its brakes are applied to slow it down to 30 km/h. An antiskid braking system limits the braking force to a value at which the wheels of the truck are just about to slide. Knowing that the coefficient of static friction between the road and the wheels is 0.65, determine the shortest time needed for the truck to slow down.arrow_forwardThe carnival ride from Prob 12.51 is modified so that the 80-kg riders can move up and down the inclined wall as the speed of the ride increases. Knowing that the coefficient of static friction between the wall and the platform is 0.2, determine the range of values of the constant speed v0 for which the platform will remain at h = 1.5 m.Reference to Problem 12.51:arrow_forwardIn the braking test of a sports car its velocity is reduced from 70 mi/h to zero in a distance of 170 ft with slipping impending. Knowing that the coefficient of kinetic friction is 80 percent of the coefficient of static friction, determine (a) the coefficient of static friction, (b) the stopping distance for the same initial velocity if the car skids. Ignore air resistance and rolling resistance.arrow_forward
- The coefficients of friction between the load and the flatbed trailer shown are μs = 0.40 and μk = 0.35. Knowing that the speed of the rig is 55 mi/h, determine the shortest time in which the rig can be brought to a stop if the load is not to shift.arrow_forwardKnowing that the coefficients of friction between the component I and member BC of the mechanism of Prob. 12.62 are μk = 0.35 and = 0.25, determine (μk a) the maximum allowable constant speed VB if the component is not to slide on BC while being transferred, (b) the values of 0 for which sliding is impending.Reference to Problem 12.62:arrow_forwardSolve Prob. 12.13, assuming that the coefficients of friction between block A and the incline are μs= 0.25 and μk= 0.20.Reference to Problem 12.13:The two blocks shown are originally at rest. Neglecting the masses of the pulleys and the effect of friction in the pulleys and between block A and the incline, determine (a) the acceleration of each block, (b) the tension in the cable.arrow_forward
- In order to determine the weight of a freight train of 40 identical boxcars, an engineer attaches a dynamometer between the train and the locomotive. The train starts from rest, travels over a straight, level track, and reaches a speed of 30 mi/h after three minutes. During this time interval, the average reading of the dynamometer is 120 tons. Knowing that the effective coefficient of friction in the system is 0.03 and air resistance is negligible, determine (a) the weight of the train (in tons), (b) the coupling force between boxcars A and B.arrow_forwardA polisher is started so that the fleece along the circumference undergoes a constant tangential acceleration of 4 m/s2 . Three seconds after it is started, small tufts of fleece from along the circumference of the 225-mm-diameter polishing pad are observed to fly free of the pad. At this instant, determine (a) the speed v of a tuft as it leaves the pad, (b ) the magnitude of the force required to free a tuft if the average mass of a tuft is 1.6 mg.arrow_forwardAt an intersection, car B was traveling south and car A was traveling 30° north of east when they slammed into each other. Upon investigation it was found that after the crash the two cars got stuck and skidded off at an angle of 10° north of east. Each driver claimed that he was going at the speed limit of 50 km/h and that he tried to slow down but couldn’t avoid the crash because the other driver was going a lot faster. Knowing that the masses of cars A and B were 1500 kg and 1200 kg, respectively, determine (a) which car was going faster, (b) the speed of the faster of the two cars if the slower car was traveling at the speed limit.arrow_forward
- To unload a bound stack of plywood from a truck, the driver first tilts the bed of the truck and then accelerates from rest. Knowing that the coefficients of friction between the bottom sheet of plywood and the bed are μs= 0.40 and μk= 0.30, determine (a) the smallest acceleration of the truck which will cause the stack of plywood to slide, (b) the acceleration of the truck which causes corner A of the stack to reach the end of the bed in 0.9 s.arrow_forwardA 2000-kg automobile starts from rest at point A on a 6° incline and coasts through a distance of 50 m to point B. The brakes are then applied, causing the automobile to come to a stop at point C, 20 m from B. Knowing that slipping is impending during the braking period and neglecting air resistance and rolling resistance, determine the speed of the automobile at point B. The speed of the automobile at point B is ___ m/s.arrow_forwardA spring AB of constant k is attached to a support at A and to a collar of mass m. The unstretched length of the spring is 1 . Knowing that the collar is released from rest at x=x0 and neglecting friction between the collar and the horizontal rod, determine the magnitude of the velocity of the collar as it passes through point C.arrow_forward
- Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
- Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY