Explanation Given: The weight is 3 lb . The radial distance ( r ) is 4 / ( 1 − cos θ ) . The transverse distance ( θ ) is 90 ° . The angular velocity ( θ ˙ ) is 4 rad/s . Write the expression for the radial distance ( r ) . r = 4 / ( 1 − cos θ ) (I). Write the expression for the transverse distance ( θ ) . θ = 45 ° = 45 ° π 180 ° = 0.785 rad Write the expression for the angular velocity ( θ ˙ ) . θ ˙ = 4 rad/s (II). Write the expression for angle ψ . tan ψ = r d r d θ (III). The radial co-ordinate is r and rate of change of radial distance with respect to angle. Write the expression for the radial acceleration. a r = r ¨ − r θ ˙ 2 (IV). Here, radial acceleration is a r and second time derivative of radius ( r ) is r ¨ . Write the expression for the transverse acceleration. a θ = r θ ¨ + 2 r ˙ θ ˙ (V). Here, transverse acceleration is a θ and second time derivative of θ is θ ¨ and first time derivative of radius ( r ) is r ˙ . Differentiate Equation (I). r = 4 / ( 1 − cos θ ) r ˙ = − 4 sin θ θ ˙ ( 1 − cos θ ) 2 (VI). Differentiate Equation (VI). r ˙ = − 4 sin θ θ ˙ ( 1 − cos θ ) 2 r ¨ = − 4 sin θ θ ¨ ( 1 − cos θ ) 2 + − 4 cos θ ( θ ˙ ) 2 ( 1 − cos θ ) 2 + 8 sin 2 θ ( θ ˙ ) 2 ( 1 − cos θ ) 3 (VII). Differentiate Equation (II). θ ˙ = 4 rad/s θ ¨ = 0 Draw the free body diagram of motorcycle as shown in Figure (1). Refer Figure (1) write the formula for equation of motion. ∑ F r = m a r (VIII). Here, summation of total force acting on radial direction is ∑ F r mass is m and acceleration radial direction is a r . Refer Figure (1) calculate the components of force. ∑ F r = P sin 45 ° − N cos 45 ° (IX). Refer Figure (1) write the formula for equation of motion. ∑ F θ = m a θ (X). Here, summation of total force acting on transverse direction is ∑ F θ mass is m and acceleration in the transverse direction is a θ . Refer Figure (1) calculate the components of force. ∑ F θ = − P cos 45 ° − N sin 45 ° (XI). Write the expression for mass. m = W 32.2 ft/s 2 (XII). Conclusion: Substitute 3 lb for W in Equation (XII). m = W 32.2 ft/s 2 = 3 lb 32.2 ft/s 2 Substitute 90 ° for θ in Equation (I). r = 4 / ( 1 − cos θ ) = 4 / ( 1 − cos 90 ° ) = 4 ft Substitute 90 ° for θ and 4 rad/s for θ ˙ in Equation (VI). r ˙ = − 4 sin θ θ ˙ ( 1 − cos θ ) 2 r ˙ = − 4 sin 90 ° ( 4 ) ( 1 − cos 90 ° ) 2 = − 16 ft/s Substitute 90 ° for θ , 0 for θ ¨ and 4 rad/s for θ ˙ in Equation (VII). r ¨ = − 4 sin θ θ ¨ ( 1 − cos θ ) 2 + − 4 cos θ ( θ ˙ ) 2 ( 1 − cos θ ) 2 + 8 sin 2 θ ( θ ˙ ) 2 ( 1 − cos θ ) 3 r ¨ = − 4 sin 90 ° θ ¨ ( 1 − cos 90 ° ) 2 + − 4 cos 90 ° ( 4 ) 2 ( 1 − cos 90 ° ) 2 + 8 sin 2 90 ° ( 4 ) 2 ( 1 − cos 90 ° ) 3 = 128 ft/s 2 Substitute 4 / ( 1 − cos θ ) for r in Equation (III)

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Chapter 13.6, Problem 108P

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The tangential retarding force P and the normal force N acting on the collar when θ=90° .

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Chapter 13.6, Problem 107P

Chapter 13.6, Problem 109P

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Ch. 13.4 - In each case, determine its velocity when t = 2 s...Ch. 13.4 - In each case, determine its velocity at s = 8 m if...Ch. 13.4 - Determine the initial acceleration of the 10-kg...Ch. 13.4 - Write the equations of motion in the x and y...Ch. 13.4 - The motor winds n the cable with a constant...Ch. 13.4 - If motor M exerts a force of F = (10t2 + 100) N on...Ch. 13.4 - A spring of stiffness k = 500 N/m is mounted...Ch. 13.4 - The spring has a stiffness k = 200 N/m and is...Ch. 13.4 - Block B rests upon a smooth surface. If the...Ch. 13.4 - The 6-lb particle is subjected to the action of...

Ch. 13.4 - The two boxcars A and B have a weight of 20 000 lb...Ch. 13.4 - If the coefficient of kinetic friction between the...Ch. 13.4 - If the 50-kg crate starts from rest and achieves a...Ch. 13.4 - If blocks A and B of mass 10 kg and 6 kg...Ch. 13.4 - The 10-lb block has a speed of 4 ft/s when the...Ch. 13.4 - The 10-lb block has a speed of 4 ft/s when the...Ch. 13.4 - The speed of the 3500-lb sports car is plotted...Ch. 13.4 - The conveyor belt is moving at 4 m/s. If the...Ch. 13.4 - The conveyor belt is designed to transport...Ch. 13.4 - Determine the time needed to pull the cord at B...Ch. 13.4 - Cylinder B has a mass m and is hoisted using the...Ch. 13.4 - Block A has a weight of 8 lb and block B has a...Ch. 13.4 - The 2-Mg truck is traveling at 15 m/s when the...Ch. 13.4 - The motor lifts the 50-kg crate with an...Ch. 13.4 - The 75-kg man pushes on the 150-kg crate with a...Ch. 13.4 - The coefficient of kinetic friction is k, and the...Ch. 13.4 - A 40-lb suitcase slides from rest 20 ft down the...Ch. 13.4 - Solve Prob. 13-18 if the suitcase has an initial...Ch. 13.4 - If the coefficient of kinetic friction between...Ch. 13.4 - The conveyor belt delivers each 12-kg crate to the...Ch. 13.4 - The 50-kg block A is released from rest. Determine...Ch. 13.4 - If the supplied force F = 150 N, determine the...Ch. 13.4 - A 60-kg suitcase slides from rest 5 m down the...Ch. 13.4 - Solve Prob. 13-24 if the suitcase has an initial...Ch. 13.4 - The 1.5 Mg sports car has a tractive force of F =...Ch. 13.4 - The conveyor belt is moving downward at 4 m/s. If...Ch. 13.4 - At the instant shown the 100-lb block A is moving...Ch. 13.4 - Determine the velocity of the 200-lb crate when t...Ch. 13.4 - Determine the velocity of the 400-kg crate A when...Ch. 13.4 - The tractor is used to lift the 150-kg load B with...Ch. 13.4 - If the tractor travels to the right with an...Ch. 13.4 - Block A and B each have a mass m. Determine the...Ch. 13.4 - The 4-kg smooth cylinder is supported by the...Ch. 13.4 - The coefficient of static friction between the...Ch. 13.4 - If the spring is unstretched when s = 0 and the...Ch. 13.4 - Neglecting the mass of the rope and pulley, and...Ch. 13.4 - Determine the force in the cable when t = 5 s, if...Ch. 13.4 - An electron of mass m is discharged with an...Ch. 13.4 - The 400-lb cylinder at A is hoisted using the...Ch. 13.4 - What is their velocity at this instant?Ch. 13.4 - Block A has a mass mA and is attached to a spring...Ch. 13.4 - A parachutist having a mass m opens his parachute...Ch. 13.4 - Neglect the mass of the motor and pulleys.Ch. 13.4 - If the force exerted on cable AB by the motor is F...Ch. 13.4 - Blocks A and B each have a mass m. Determine the...Ch. 13.4 - Blocks A and Beach have a mass m. Determine the...Ch. 13.4 - If the board AC pushes on the block at an angle ...Ch. 13.4 - If a horizontal force P = 12lb is applied to block...Ch. 13.4 - A freight elevator, including its load, has a mass...Ch. 13.4 - The block A has a mass mA and rests on the pan B,...Ch. 13.5 - P13-5.Set up the n, t axes and write the equations...Ch. 13.5 - P13-6.Set up the n, b, t axes and write the...Ch. 13.5 - The block rests at a distance of 2 m from the...Ch. 13.5 - Prob. 8FP Ch. 13.5 - A pilot weighs 150 lb and is traveling at a...Ch. 13.5 - The sports car is traveling along a 30 banked road...Ch. 13.5 - If the 10-kg ball has a velocity of 3m/ s when it...Ch. 13.5 - The motorcycle has a mass of 0.5 Mg and a...Ch. 13.5 - Prob. 52P Ch. 13.5 - Prob. 53P Ch. 13.5 - The 2-kg block B and 15-kg cylinder A are...Ch. 13.5 - Determine the maximum constant speed at which the...Ch. 13.5 - Cartons having a mass of 5 kg are required to move...Ch. 13.5 - Prob. 57P Ch. 13.5 - Prob. 58P Ch. 13.5 - Prob. 59P Ch. 13.5 - Prob. 60P Ch. 13.5 - At the instant B = 60, the boys center of mass G...Ch. 13.5 - A girl having a mass of 25 kg sits at the edge of...Ch. 13.5 - The pendulum bob B has a weight of 5 lb and is...Ch. 13.5 - The pendulum bob B has a mass m and is released...Ch. 13.5 - Determine the constant speed of the passengers on...Ch. 13.5 - A motorcyclist in a circus rides his motorcycle...Ch. 13.5 - The vehicle is designed to combine the feel of a...Ch. 13.5 - The 0.8-Mg car travels over the hill having the...Ch. 13.5 - The 0.8-Mg car travels over the hill having the...Ch. 13.5 - When it reaches the curved portion AB, it is...Ch. 13.5 - Determine the resultant normal and frictional...Ch. 13.5 - If he rotates about the z axis with a constant...Ch. 13.5 - Determine the maximum speed at which the car with...Ch. 13.5 - Determine the maximum constant speed at which the...Ch. 13.5 - The box has a mass m and slides down the smooth...Ch. 13.5 - Prove that if the block is released from rest at...Ch. 13.5 - The cylindrical plug has a weight of 2 lb and it...Ch. 13.5 - When crossing an intersection, a motorcyclist...Ch. 13.5 - The airplane, traveling at a constant speed of 50...Ch. 13.5 - The 2-kg pendulum bob moves in the vertical plane...Ch. 13.5 - The 2-kg pendulum bob moves in the vertical plane...Ch. 13.5 - If it has a speed of 1.5 m/s when y = 0.2 m,...Ch. 13.5 - The ball has a mass m and is attached to the cord...Ch. 13.6 - If the attached spring has a stiffness k = 2...Ch. 13.6 - Determine the constant angular velocity of the...Ch. 13.6 - If = ( t2) rad, where t is in seconds, determine...Ch. 13.6 - The 2-Mg car is traveling along the curved road...Ch. 13.6 - The 0.2-kg pin P is constrained to move in the...Ch. 13.6 - If the cam is rotating at a constant rate of 6...Ch. 13.6 - Determine the magnitude of the resultant force...Ch. 13.6 - Determine the magnitude of the unbalanced force...Ch. 13.6 - Rod OA rotates counterclockwise with a constant...Ch. 13.6 - The boy of mass 40 kg is sliding down the spiral...Ch. 13.6 - Using a forked rod, a 0.5-kg smooth peg P is...Ch. 13.6 - The arm is rotating at a rate of = 4 rad/s when ...Ch. 13.6 - If arm OA rotates with a constant clockwise...Ch. 13.6 - Determine the normal and frictional driving forces...Ch. 13.6 - A smooth can C, having a mass of 3 kg, is lifted...Ch. 13.6 - Prob. 96P Ch. 13.6 - Prob. 97P Ch. 13.6 - The particle has a mass of 0.5 kg and is confined...Ch. 13.6 - A car of a roller coaster travels along a track...Ch. 13.6 - The 0.5-lb ball is guided along the vertical...Ch. 13.6 - The ball of mass misguided along the vertical...Ch. 13.6 - Using a forked rod, a smooth cylinder P, having a...Ch. 13.6 - The pilot of the airplane executes a vertical loop...Ch. 13.6 - The collar has a mass of 2 kg and travels along...Ch. 13.6 - The particle has a mass of 0.5 kg and is confined...Ch. 13.6 - Solve Prob. 13-105 If the arm has an angular...Ch. 13.6 - The forked rod is used to move the smooth 2-lb...Ch. 13.6 - Prob. 108P Ch. 13.6 - Rod OA rotates counterclockwise at a constant...Ch. 13.6 - Solve Prob. 13-109 if motion is in the vertical...Ch. 13.7 - If his speed is a constant vP = 80 ft/s, determine...Ch. 13.7 - The earth has an orbit with eccentricity 0.0167...Ch. 13.7 - Prob. 114P Ch. 13.7 - Determine the speed of a satellite launched...Ch. 13.7 - Prob. 116P Ch. 13.7 - Prove Keplers third law of motion. Hint: Use Eqs....Ch. 13.7 - Prob. 118P Ch. 13.7 - Prob. 119P Ch. 13.7 - Determine the constant speed of satellite S so...Ch. 13.7 - Prob. 121P Ch. 13.7 - Prob. 122P Ch. 13.7 - Prob. 123P Ch. 13.7 - Prob. 124P Ch. 13.7 - The rocket is traveling around the earth in free...Ch. 13.7 - Prob. 127P Ch. 13.7 - Prob. 128P Ch. 13.7 - Prob. 129P Ch. 13.7 - Prob. 130P Ch. 13.7 - The rocket is traveling around the earth in free...Ch. 13.7 - Prob. 132P Ch. 13.7 - Prob. 3CP Ch. 13.7 - If the trailer has a mass of 250 kg and coasts 45...Ch. 13.7 - The coefficient of kinetic friction between the...Ch. 13.7 - Block B rests on a smooth surface. If the...Ch. 13.7 - If the motor draws in the cable at a rate of v =...Ch. 13.7 - The ball has a mass of 30 kg and a speed v = 4 m/s...Ch. 13.7 - If the coefficient of static friction between the...Ch. 13.7 - If at the instant it reaches point A it has a...

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The tangential retarding force P and the normal force N acting on the collar when θ = 90 ° .

Solution Summary: The author calculates the tangential retarding force and normal force of the collar when theta = 45°.

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The tangential retarding force P and the normal force N acting on the collar when θ=90° .

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Chapter 13 Solutions