Energy
The 30-kg box is sliding down the smooth surface at 1 m/s when it is in position 1. Determine the difference in magnitudes of the box’s velocity at position 2 between the two cases.
0 m/s
The 2000-lb drag racer starts from rest and travels a quarter-mile course. It completes the course in 4.524 seconds and crosses the finish line traveling at 325.77 mi/h. Determine the constant horizontal force exerted on the car during the race.
5370 lb
An automobile having a mass of 2 Mg travels up a 7° slope at a constant speed of v = 100 km/h. If mechanical friction and wind resistance are neglected, determine the power developed by the engine.
66418 W
The object consists of an 8-lb slender bar welded to a circular disk. When the object is released from rest in position 1, its angular velocity in position 2 is 4.6 rad/s. What is the weight of the disk?
22.2 lb
Water leaves the nozzle at 20◦ above the horizontal and strikes the wall at the point indicated. What was the velocity of the water as it left the nozzle?
68.6 ft/s
To design a bumper using a linear spring that will bring a 50-lb box moving at 10 ft/s to rest 6 inches from the point of contact with bumper, what is the necessary spring constant k? (neglect friction)
621.7 lb/ft
The system is released from rest. The 4-kg mass slides on the smooth horizontal surface. Determine the magnitude of the velocity of the masses when the 20-kg mass has fallen 1 m. The coefficient of kinetic friction between the 4-kg mass and the horizontal surface is μk = 0.4.
3.88 m/s
The man having the weight of 150 lb is able to run up a 15-ft-high fight of stairs in 4 s. Determine the power generated by the man.
562.5 ft-lb/s or 1 hp
If the angular velocity of the satellite in configuration (a) is 4 rpm, determine the distance d in configuration (b) that will cause the angular velocity to be 1 rpm. The moment of inertia of the satellite is I = 500 kg-m2 and each mass is 2 kg. (Assume that the cables and masses rotate with the same angular velocity as the satellite. Neglect the masses of the cables and the mass moments of inertia of the masses about their centers of mass.)
19.8 m
A baseball bat (shown with the bat’s axis perpendicular to the page) strikes a thrown baseball. Before their impact, the velocity of the baseball is vb = 132(cos 45◦i + cos 45◦j) (ft/s) and the velocity of the bat is vB =60(−cos45◦i−cos45◦j)(ft/s). Neglect the change in the velocity of the bat due to the direct central impact. The coefficient of restitution is e = 0.2. What is the ball’s velocity vector after the impact?
(−69.6i + 93.3j) ft/s
The system is released from rest with the spring unstretched. The spring constant k = 200 N/m. Determine the magnitude of the velocity of the masses when the right mass has fallen 1 m.
2.18 m/s
The Union Pacific Big Boy locomotive weighs 1.19 million lb, and the traction force (tangential force) of its drive wheels is 135,000 lb. If you neglect other tangential forces, what distance is required for the train to accelerate from zero to 60 mi/h?
1061 ft
The Union Pacific Big Boy locomotive weighs 1.19 million lb, and the traction force (tangential force) of its drive wheels is 135,000 lb. What is the maximum power transferred to the locomotive during its acceleration from zero to 60 mi/h?
11,880,000 lb-ft/s
The 2-kg bar rotates in the horizontal plane about the smooth pin. The 6-kg collar A slides on the smooth bar. Assume that the moment of inertia of the collar A about its center of mass is negligible; that is, treat the collar as a particle. At the instant shown, the angular velocity of the bar is ω = 60 rpm and the distance from the pin to the collar is r = 1.8 m. Use conservation of angular momentum to determine the bar’s angular velocity when r = 2.4 m.
37.6 rpm or 3.94 rad/s
An athlete exercises his arm by raising the 8-kg mass m. The shoulder joint A is stationary. The distance AB is 300 mm, the distance BC is 400 mm, and the distance from C to the pulley is 340 mm. The angular velocities ωAB = 1.5 rad/s and ωBC = 2 rad/s are constant. What is the tension in the cable?
83.2 N