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Chapter 13

# Chapter 13 - Engineering Mechanics Dynamics Chapter 13...

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Engineering Mechanics - Dynamics Chapter 13 Problem 13-1 Determine the gravitational attraction between two spheres which are just touching each other. Each sphere has a mass M and radius r . Given: r 200 mm M 10 kg G 66.73 10 12 0 u m 3 kg s 2 ¡ nN 1 10 9 0 u N Solution: F GM 2 2 r ( ) 2 F 41.7 nN Problem 13-2 By using an inclined plane to retard the motion of a falling object, and thus make the observations more accurate, Galileo was able to determine experimentally that the distance through which an object moves in free fall is proportional to the square of the time for travel. Show that this is the case, i.e., s v t 2 by determining the time t B , t C , and t D needed for a block of mass m to slide from rest at A to points B, C , and D , respectively. Neglect the effects of friction. Given: s B 2 m s C 4 m s D 9 m T 20 deg g 9.81 m s 2 Solution: W sin T + , W g § ¨ © · ¸ ¹ a a g sin T + , a 3.355 m s 2 s 1 2 at 2 t B 2 s B a t B 1.09 s 145

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Engineering Mechanics - Dynamics Chapter 13 t C 2 s C a t C 1.54 s t D 2 s D a t D 2.32 s Problem 13-3 A bar B of mass M 1 , originally at rest, is being towed over a series of small rollers. Determine the force in the cable at time t if the motor M is drawing in the cable for a short time at a rate v = kt 2 . How far does the bar move in time t ? Neglect the mass of the cable, pulley, and the rollers. Given: kN 10 3 N M 1 300 kg t 5 s k 0.4 m s 3 Solution: v kt 2 v 10 m s a 2 kt a 4 m s 2 T M 1 a T 1.2 kN d 0 t t kt 2 ´ µ d d 16.7 m *Problem 13-4 A crate having a mass M falls horizontally off the back of a truck which is traveling with speed v . Determine the coefficient of kinetic friction between the road and the crate if the crate slides a distance d on the ground with no tumbling along the road before coming to rest. Assume that the initial speed of the crate along the road is v . 146
Engineering Mechanics - Dynamics Chapter 13 Given: M 60 kg d 45 m v 80 km hr g 9.81 m s 2 Solution: N C M g 0 0 N C M g P k N C M a a P k g v 2 2 ad P k gd P k v 2 2 gd P k 0.559 Problem 13-5 The crane lifts a bin of mass M with an initial acceleration a . Determine the force in each of the supporting cables due to this motion. Given: M 700 kg b 3 kN 10 3 N a 3 m s 2 c 4 Solution: 2 T c b 2 c 2 . § ¨ © · ¸ ¹ M g 0 M a T M a g . ( ) b 2 c 2 . 2 c § ¨ © · ¸ ¹ T 5.60 kN 147

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Engineering Mechanics - Dynamics Chapter 13 Problem 13-6 The baggage truck A has mass m t and is used to pull the two cars, each with mass m c . The tractive force on the truck is F . Determine the initial acceleration of the truck. What is the acceleration of the truck if the coupling at C suddenly fails? The car wheels are free to roll. Neglect the mass of the wheels. Given: m t 800 kg m c 300 kg F 480 N Solution: . o 6 F x = ma x ; F m t 2 m c . + , a a F m t 2 m c . a 0.343 m s 2 . o 6 F x = ma x ; F m t m c . + , a Fail a Fail F m t m c . a Fail 0.436 m s 2 Problem 13-7 The fuel assembly of mass M for a nuclear reactor is being lifted out from the core of the nuclear reactor using the pulley system shown. It is hoisted upward with a constant acceleration such that s = 0 and v = 0 when t = 0 and s = s 1 when t = t 1 . Determine the tension in the cable at
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Chapter 13 - Engineering Mechanics Dynamics Chapter 13...

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