Chapter 15 - Engineering Mechanics - Dynamics Chapter 15...

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Unformatted text preview: Engineering Mechanics - Dynamics Chapter 15 Problem 15-1 A block of weight W slides down an inclined plane of angle T# with initial velocity v . Determine the velocity of the block at time t 1 if the coefficient of kinetic friction between the block and the plane is P k . Given: W 20 lb t 1 3 s T 30 deg P k 0.25 v 2 ft s g 32.2 ft s 2 Solution: ( ) m v y1 6 t 1 t 2 t F y' ´ µ ¶ d . m v y2 F N t 1 . W cos T + , t 1 F N W cos T + , F N 17.32 lb ( ) m v x'1 + , 6 t 1 t 2 t F x' ´ µ ¶ d . m v x'2 + , W g § © · ¹ v W sin T + , t 1 . P k F N t 1 W g § © · ¹ v v W v W sin T + , t 1 g P k F N t 1 g . W v 29.4 ft s Problem 15-2 A ball of weight W is thrown in the direction shown with an initial speed v A . Determine the time needed for it to reach its highest point B and the speed at which it is traveling at B . Use the principle of impulse and momentum for the solution. Given: W 2 lb T 30 deg v A 18 ft s g 32.2 ft s 2 302 Engineering Mechanics - Dynamics Chapter 15 Solution: W g § © · ¹ v A sin T + , W t W g § © · ¹ t v A sin T + , g t 0.280 s W g § © · ¹ v A cos T + , . W g § © · ¹ v x v x v A cos T + , v x 15.59 ft s Problem 15-3 A block of weight W is given an initial velocity v up a smooth slope of angle T . Determine the time it will take to travel up the slope before it stops. Given: W 5 lb v 10 ft s T 45 deg g 32.2 ft s 2 Solution: W g § © · ¹ v W sin T + , t t v g sin T + , t 0.439 s * Problem 15-4 The baseball has a horizontal speed v 1 when it is struck by the bat B . If it then travels away at an angle T from the horizontal and reaches a maximum height h , measured from the height of the bat, determine the magnitude of the net impulse of the bat on the ball.The ball has a mass M . Neglect the weight of the ball during the time the bat strikes the ball. Given: M 0.4 kg v 1 35 m s h 50 m T 60 deg g 9.81 m s 2 303 Engineering Mechanics - Dynamics Chapter 15 Solution: Guesses v 2 20 m s Imp x 1 N s ¢ Imp y 10 N s ¢ Given 1 2 M v 2 sin T + , + , 2 M g h M v 1 Imp x . M v 2 cos T + , Imp y . M v 2 sin T + , v 2 Imp x Imp y § ¨ ¨ © · ¸ ¸ ¹ Find v 2 Imp x / Imp y / + , v 2 36.2 m s Imp x Imp y § ¨ © · ¸ ¹ 21.2 12.5 § © · ¹ N s ¢ Imp x Imp y § ¨ © · ¸ ¹ 24.7 N s ¢ Problem 15-5 The choice of a seating material for moving vehicles depends upon its ability to resist shock and vibration. From the data shown in the graphs, determine the impulses created by a falling weight onto a sample of urethane foam and CONFOR foam. Units Used: ms 10 3 s Given: F 1 0.3 N t 1 2 ms F 2 0.4 N t 2 4 ms F 3 0.5 N t 3 7 ms F 4 0.8 N t 4 10 ms F 5 1.2 N t 5 14 ms Solution: CONFOR foam: I c 1 2 t 1 F 3 1 2 F 3 F 4 . + , t 3 t 1 + , ....
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