Explanation Given: The total mass of the car with passengers is m = 700 kg . The initial velocity of the car at hill A is v A = 3 m/s . The radius of the loop B is ρ B = 7.5 m . The radius of the loop C is ρ C = 5 m . The height of the B is h B = 15 m . The height of the C is h C = 10 m . Draw the free body diagram of the car as shown Figure (1). Refer Figure (1). The car experiences the centripetal normal acceleration at B and C . Write the formula centripetal normal acceleration. ( a n ) B = v B 2 ρ B (I) ( a n ) C = v C 2 ρ C (II) Here, v is the velocity and ρ is the radius of track loop. Write the formula for kinetic energy. T = 1 2 m v 2 Write the formula for potential energy. V = m g h Here, m is the mass, g is the acceleration due to gravity and h is the elevation of the object from the datum. Write the formula for conservation of Energy. T 1 + V 1 = T 2 + V 2 Substitute 1 2 m v 1 2 for T 1 , 1 2 m v 2 2 for T 2 , m g h 1 for V 1 and m g h 2 for V 2 . 1 2 m v 1 2 + m g h 1 = 1 2 m v 2 2 + m g h 2 (III) Here, T is kinetic energy, V is potential energy and the suffixes 1 , 2 indicates the initial and final stages. Conclusion: Refer Figure (1). Consider the coaster car is at B . Resolve the forces along n − a x i s . ∑ F n = m ( a n ) B − N B − W = m ( v B 2 ρ B ) Substitute 700 ( 9.81 ) N for W , 700 kg for m and 7.5 m for ρ B . − N B − 700 ( 9.81 ) N = − ( 700 kg ) ( v B 2 7.5 m ) (IV) Consider the coaster car is at C . Resolve the forces along n − a x i s . ∑ F n = m ( a n ) C − N C − W = m ( v C 2 ρ C ) Substitute 700 ( 9.81 ) N for W , 700 kg for m and 5 m for ρ C . − N C − 700 ( 9.81 ) N = − ( 700 kg ) ( v C 2 5 m ) (V) When the coaster car leaves the loop at B , the normal reaction N B becomes zero. Substitute 0 for N B in Equation (IV). − 0 − 700 ( 9.81 ) N = − ( 700 kg ) ( v B 2 7.5 m ) − 6867 = − 93.3333 v B 2 v B 2 = 6867 93.3333 v B 2 = 73.5750 m 2 /s 2 When, the coaster car leaves the loop at C , the normal reaction N C becomes zero Substitute 0 for N C in Equation (V). − 0 − 700 ( 9.81 ) N = − ( 700 kg ) ( v C 2 5 m ) − 6867 = − 140 v B 2 v C 2 = 6867 140 v C 2 = 49

Engineering Mechanics: Dynamics (14th Edition)

14th Edition

ISBN: 9780133915389

Author: Russell C. Hibbeler

Publisher: PEARSON

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Chapter 14.5, Problem 72P

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The minimum height h of the hill A and normal reactions at B, C .

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Chapter 14.5, Problem 71P

Chapter 14.5, Problem 73P

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Chapter 14 Solutions

Engineering Mechanics: Dynamics (14th Edition)

Ch. 14.3 - Determine the work of the force when it displaces...Ch. 14.3 - Determine the kinetic energy of the 10-kg block.Ch. 14.3 - The spring is placed between the wall and the...Ch. 14.3 - If the motor exerts a constant force of 300 N on...Ch. 14.3 - The crate is initially at rest on the ground.Ch. 14.3 - If the drag force of the parachute can be...Ch. 14.3 - When s = 0.5 m, the spring is unstretched and the...Ch. 14.3 - The 5-lb collar is pulled by a cord that passes...Ch. 14.3 - The 20-kg crate is subjected to a force having a...Ch. 14.3 - If the relation between the force and deflection...

Ch. 14.3 - If it is originally at rest, determine the...Ch. 14.3 - If it is originally at rest, determine the...Ch. 14.3 - Determine the required height h of the roller...Ch. 14.3 - How far will the truck skid if it is traveling 80...Ch. 14.3 - Show that this is so, by considering the 10-kg...Ch. 14.3 - A force of F = 250 N is applied to the end at B....Ch. 14.3 - If the block has a mass of 20 kg and is suspended...Ch. 14.3 - Determine how far the block must slide before its...Ch. 14.3 - If the 6-kg collar is orginally at rest, determine...Ch. 14.3 - Select the proper value of k so that the maximum...Ch. 14.3 - Determine the speed of the brick just before it...Ch. 14.3 - Determine the speed of block A after it moves 5 ft...Ch. 14.3 - If the kinetic coefficient of friction between the...Ch. 14.3 - Determine the angle at which the box leaves the...Ch. 14.3 - If the cord is subjected to a constant force of F=...Ch. 14.3 - Determine the maximum distance A will fall before...Ch. 14.3 - If the cord is subjected to a constant force of F=...Ch. 14.3 - The barrier stopping force is measured versus the...Ch. 14.3 - The coefficient of kinetic friction between both...Ch. 14.3 - If the coefficient of kinetic friction between the...Ch. 14.3 - The 8-Kg block is moving with an initial speed of...Ch. 14.3 - At a given instant the 10-lb block A is moving...Ch. 14.3 - The 5-lb cylinder is falling from A with a speed...Ch. 14.3 - The propelling action is obtained by drawing the...Ch. 14.3 - By design the car cannot fall off the track,...Ch. 14.3 - If the coefficient of kinetic friction along AB is...Ch. 14.3 - Prob. 29P Ch. 14.3 - If the can is prevented from moving, determine the...Ch. 14.3 - Determine the placement R of the can from the end...Ch. 14.3 - If it starts from rest when the attached spring is...Ch. 14.3 - Neglect the size of the block.Ch. 14.3 - As shown, the spring is confined by the plate P...Ch. 14.3 - Determine his speed when he reaches point B on the...Ch. 14.3 - As shown, it is confined by the plate and wall...Ch. 14.3 - If the track is to be designed so that the...Ch. 14.3 - Neglect friction.Ch. 14.3 - Neglect friction and the size of the pulley.Ch. 14.3 - Neglect friction and the size of the pulley.Ch. 14.3 - An elastic cord having a stiffness k = 2 lb/ft is...Ch. 14.4 - In initially, the block is at rest.Ch. 14.4 - When s = 0, the 20-kg block is moving at v = 1...Ch. 14.4 - The load weighs 100 lb and the efficiency of the...Ch. 14.4 - If the block is traveling up the inclined plane...Ch. 14.4 - determine the power input to the motor, which...Ch. 14.4 - which is increasing at a rate of aP = 6 m/s2....Ch. 14.4 - Assuming the wheels do not slip on the ground,...Ch. 14.4 - Determine the power Input for a motor necessary to...Ch. 14.4 - If mechanical friction and wind resistance are...Ch. 14.4 - manufactures a turbojet engine that is placed in a...Ch. 14.4 - If the car is brought to a stop, determine how...Ch. 14.4 - If the steps are 125 mm high and 250 mm in length,...Ch. 14.4 - Determine the power generated. 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Also,...Ch. 14.5 - Prob. 83P Ch. 14.5 - The spring has an unstretched length of 1 m.Ch. 14.5 - A 60-kg satellite travels in free flight along an...Ch. 14.5 - If friction and air resistance can be neglected,...Ch. 14.5 - If the mass of the bumpers A and B can be...Ch. 14.5 - If the collar moves over the smooth rod, determine...Ch. 14.5 - When the 6-kg box reaches point A it has a speed...Ch. 14.5 - Determine the normal force the box exerts on the...Ch. 14.5 - Determine how high the box reaches up the surface...Ch. 14.5 - Determine the cars velocity and the normal force...Ch. 14.5 - The 10-kg sphere C is released from rest when =...Ch. 14.5 - If the chain is released from rest from the...Ch. 14.5 - Each spring has a stiffness k = 40 N/m and an...Ch. 14.5 - Prob. 96P Ch. 14.5 - Initially each spring has a tension of 50 N Ch. 14.5 - Determine the approximate normal force it exerts...Ch. 14.5 - If a 150-lb crate is released from rest at A,...Ch. 14.5 - During the motion, the collar is acted upon by a...Ch. 14.5 - Determine the speed at which it slides off at B....Ch. 14.5 - If the block starts from rest when the attached...Ch. 14.5 - Prob. 5RP Ch. 14.5 - The motor has an efficiency of = 0.76.Ch. 14.5 - If the collar is released from rest at A and...Ch. 14.5 - respectively. 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The minimum height h of the hill A and normal reactions at B , C .

Solution Summary: The author calculates the minimum height of the hill A and normal reactions at B on the coaster car.

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Chapter 14 Solutions