Mass and Gravitational Potential Energy
WORK and ENERGY Work done by a constant force 1-The drawing shows a plane diving toward the ground and then climbing back upward. During each of these motions, the lift force acts perpendicular to the displacement , which has the same magnitude, 1. 7 ? 103 m, in each case. The engines of the plane exert a thrust , which points in the direction of the displacement and has the same magnitude during the dive and the climb. The weight of the plane has a magnitude of 5. 9 ? 104 N. In both motions, net work is performed due to the combined action of the forces , and . a. Is more net work done during the dive or the climb?
Explain. b. Find the difference between the net work done during the dive and the climb. Answer: a. More net work is done during the dive. b. 6. 8 ? 107 J 2- Find the work done by a force through a displacement of 3m in the positive x direction Work-Energy theorem and kinetic energy 3-The mass of the space probe is 474-kg and its initial velocity is 275 m/s. If the 56. 0-mN force acts on the probe through a displacement of 2. 42? 109m, what is its final speed? Answer: 4-Example 2: Skier Gravitational Potential Energy, Conservative versus Nonconservative Forces 5-The gymnast leaves the trampoline at an initial height of 1. 0 m and reaches a maximum height of 4. 80 m before falling back down. What was the initial speed of the gymnast? Answer: 6-A man lifts a book of mass 0. 45 kg at a constant speed from a shelf 1. 2 m high to a shelf 2 m high 1) calculate: a)The change in PE b)The work done by the man c)The work done by gravity 2) If the book falls down from the second shelf, calculate its speed as it passes the first shelf, and its speed when it hits the ground. The Conservation of Mechanical Energy 7-A motorcyclist is trying to leap across the canyon by driving horizontally off a cliff 38. 0 m/s.
Ignoring air resistance, find the speed with which the cycle strikes the ground on the other side. Answer: 8-The skateboarder in the drawing starts down the left side of the ramp with an initial speed of 5. 4 m/s. If nonconservative forces, such as kinetic friction and air resistance, are negligible, what would be the height h of the highest point reached by the skateboarder on the right side of the ramp? 9-The drawing shows a person who, starting from rest at the top of a cliff, swings down at the end of a rope, releases it, and falls into the water below. There are two paths by which the person can enter the water.
Suppose he enters the water at a speed of 13. 0 m/s via path 1. How fast is he moving on path 2 when he releases the rope at a height of 5. 20 m above the water? Ignore the effects of air resistance. 10-The figure below illustrates the motion of a mass m = 300 kg as it slides along a track, which has smooth segments (frictionless). If the mass was released from rest at point A on the track, fill the table below. PEKEMEv A B C D E Nonconservative Forces and the Work–Energy Theorem 11-The 8 kg mass shown in the Figure moves 5 m up an inclined (? = 30o) rough surface (? k= 0. 2) as a result of the applied tension (T = 40N).
If the mass started from rest and neglecting the masses of the pulley and the string, find: a. The work done by the frictional force b. The work done by gravitational force c. The work done by tension d. The speed of the object at the end of its motion 12-From point A to B on the rough surface, the cyclist lost 2000J of energy due to the frictional force of the rough surface of the 10 m road. She started with an initial speed vA at point A, arriving at point B with a speed of vB. The cyclist barely made it to the flat part (point C) of the frictionless surface without pedaling.
If the weight of the bike and the cyclist is 980N, and point C is located at h = 0. 5 m above the ground, find: a. The speed of cyclist at point B, vB b. The speed of cyclist at point A, vA c. The coefficient of kinetic friction, µk , between the bike tires and the road. 13-The figure below depicts the motion of a mass m = 300 kg as it slides along a track, which has one smooth segment and two rough segments of kinetic friction coefficient of 0. 4. If the mass was released from rest at point A on the track, a. Find the point where the KE of the mass is zero (i. e. oint E where the mass comes to a complete stop) b. Plot (draw) the kinetic energy of the 300 kg mass as a function of position from point A until point D. [Show all work, use proper scale, show equations and substitution with units and show all points on the graph]. 14-The ambulance shown in the figure below (3000 kg) slides down a frictionless incline that is 10m long. It starts from rest at point A. Then it continues along a rough surface (BC) until it comes to a complete stop at point C. a. Calculate its speed at point B b. If the coefficient of kinetic friction of the rough segment (BC) is 0. , calculate the distance d the ambulance slides on before stopping. Power 15-Bicyclists in the Tour de France do enormous amounts of work during a race. For example, the average power per kilogram generated by Lance Armstrong (m = 75. 0 kg) is 6. 50 W per kilogram of his body mass. a. How much work does he do during a 135-km race in which his average speed is 12. 0 m/s? b. Often, the work done is expressed in nutritional Calories rather than in joules. Express the work done in part (a) in terms of nutritional Calories, noting that 1 joule = 2. 389 ? 10-4 nutritional Calories. 16-You are working out on a rowing machine.
Each time you pull the rowing bar toward you, it moves a distance of 1. 2 m in a time of 1. 5 s. The readout on the display indicates that the average power you are producing is 82 W. What is the magnitude of the force that you exert on the handle Graphical analysis 17- The graph below represents the kinetic energy, gravitational potential energy, and total mechanical energy of a moving block. Which statement best describes the motion of the block? a) Accelerating on a flat horizontal surface b) Sliding up a frictionless incline c) Falling freely d) Being lifted at constant velocity e) A fluid flowing in a river
