Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Photoelectric effect wikipedia , lookup
Eigenstate thermalization hypothesis wikipedia , lookup
Centripetal force wikipedia , lookup
Internal energy wikipedia , lookup
Rotating locomotion in living systems wikipedia , lookup
Kinetic art wikipedia , lookup
Thermodynamic temperature wikipedia , lookup
Relativistic mechanics wikipedia , lookup
PROBLEM 13.3 A baseball player hits a 5.1-oz baseball with an initial velocity of 140 ft/s at an angle of 40° with the horizontal as shown. Determine (a) the kinetic energy of the ball immediately after it is hit, (b) the kinetic energy of the ball when it reaches its maximum height, (c) the maximum height above the ground reached by the ball. SOLUTION Mass of baseball: (a) W (5.1 oz) m W g 1 lb 16 oz 0.31875 lb 32.2 ft/s 2 0.31875 lb 0.009899 lb s 2 /ft Kinetic energy immediately after hit. v v0 140 ft/s T1 (b) 1 2 mv 2 1 (0.009899)(140)2 2 T1 97.0 ft lb T2 56.9 ft lb Kinetic energy at maximum height: v v0 cos 40 1 2 mv 2 T2 Principle of work and energy: Work of weight: 140cos 40 T1 U1 2 107.246 ft/s 1 (0.009899)(107.246)2 2 T2 U1 2 T2 T1 U1 2 Wd 40.082 ft lb Maximum height above impact point. d (c) T2 T1 W 40.082 ft lb 125.7 ft 0.31875 lb 125.7 ft Maximum height above ground: h 125.7 ft 2 ft h 127.7 ft Copyright © McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 13.9 A package is projected up a 15 incline at A with an initial velocity of 8 m/s. Knowing that the coefficient of kinetic friction between the package and the incline is 0.12, determine (a) the maximum distance d that the package will move up the incline, (b) the velocity of the package as it returns to its original position. SOLUTION (a) Up the plane from A to B: TA UA B F UA B TA U A B 1 2 1W W mv A (8 m/s)2 32 2 2 g g ( W sin15 F )d F kN 0 N W cos15 W (sin15 TB : 32 W g 0 N 0 0.12 N W cos15 0.12cos15 )d Wd (0.3747) Wd (0.3743) 0 32 (9.81)(0.3747) d (b) TB d 8.70 m Down the plane from B to A: (F reverses direction) TA UB A 1W 2 vA TB 0 2 g (W sin15 F )d W (sin15 UB A 1.245W TB U B A TA d 8.71 m/s 0.12 cos15 )(8.70 m/s) 0 1.245W 1W 2 vA 2 g v A2 (2)(9.81)(1.245) vA 24.43 4.94 m/s vA 4.94 m/s Copyright © McGraw-Hill Education. Permission required for reproduction or display. 15 PROBLEM 13.17 The subway train shown is traveling at a speed of 30 mi/h when the brakes are fully applied on the wheels of cars B and C, causing them to slide on the track, but are not applied on the wheels of car A. Knowing that the coefficient of kinetic friction is 0.35 between the wheels and the track, determine (a) the distance required to bring the train to a stop, (b) the force in each coupling. SOLUTION k 0.35 FB (0.35)(100 kips) 35 kips FC v1 (a) 30 mi/h T1 U1 Entire train: 2 (0.35)(80 kips) 28 kips v2 44 ft/s 0 T2 1 (80 kips 100 kips 80 kips) (44 ft/s) 2 2 32.2 ft/s 2 (28 kips 35 kips) x x 124.07 ft (b) 0 T2 0 x 124.1 ft Force in each coupling: Recall that x 124.07 ft Car A: Assume FAB to be in tension T1 V1 1 80 kips (44) 2 2 32.2 2 FAB (124.07 ft) T2 0 19.38 kips FAB FAB T1 U1 Car C: 1 80 kips (44) 2 2 32.2 ( FBC 2 28 kips)(124.07 ft) FBC FBC 19.38 kips (tension) T2 0 28 kips 8.62 kips 19.38 kips FBC 8.62 kips (tension) Copyright © McGraw-Hill Education. Permission required for reproduction or display.