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# 8389 work 1

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### 8389 work 1

1. 1. WORK, ENERGY & POWER Directions: Solve only the problems whose numbers correspond to your group number. Example, if you belong to Group 1, solve the problems numbered 1 (A1, B1, etc.). be sure your solutions are neat and well presented. You are to submit hard copy of your solutions next week. A1. A concrete block is pulled 7.0 m across a frictionless surface by means of a rope. The tension in the rope is 40 N; and the net work done on the block is 247 J. What angle does the rope make with the horizontal? A2. Mike is cutting the grass using a human-powered lawn mower. He pushes the mower with a force of 45 N directed at an angle of 41° below the horizontal direction. Calculate the work that Mike does on the mower each time he pushes it 9.1 m across the yard. A3. A 5.00-kg block of ice is sliding across a frozen pond at 2.00 m/s. A 7.60-N force is applied in the direction of motion. After the ice block slides 15.0 m, the force is removed. Determine the work done by the applied force. A4. A force with a magnitude of 25 N and directed at an angle of 37° above the horizontal is used to move a 10-kg crate along a horizontal surface at constant velocity. How much work is done by this force in moving the crate a distance of 15 m? A5. A constant force of 25 N is applied as shown to a block which undergoes a displacement of 7.5 m to the right along a frictionless surface while the force acts. What is the work done by the force? A6. Julie carries an 8.0-kg suitcase as she walks 18 m along a horizontal walkway to her hotel room at a constant speed of 1.5 m/s. How much work does Julie do in carrying her suitcase? B1. An experimental 1500-kg car travels at a constant speed of 22 m/s around a circular test track that is 80 m across. What is the kinetic energy of the car? B2. The kinetic energy of a car is 8 × 106 J as it travels along a horizontal road. How much work is required to stop the car in 10 s? B3. How much energy is dissipated in braking a 1200-kg car to a stop from an initial speed of 30 m/s? B4. The kinetic energy of an 1800-kg truck is 7.2 × 105 J. What is the speed of the truck? B5. A 10.0-g bullet traveling horizontally at 755 m/s strikes a stationary target and stops after penetrating 14.5 cm into the target. What is the average force of the target on the bullet? B6. A car is traveling at 7.0 m/s when the driver applies the brakes. The car moves 1.5 m before it comes to a complete stop. If the car had been moving at 14 m/s, how far would it have continued to move after the brakes were applied? Assume the braking force in both cases is constant and the same.
2. 2. C1. A woman stands on the edge of a cliff and throws a stone vertically downward with an initial speed of 10 m/s. The instant before the stone hits the ground below, it has 450 J of kinetic energy. If she were to throw the stone horizontally outward from the cliff with the same initial speed of 10 m/s, how much kinetic energy would it have just before it hits the ground? C2. A 12-kg crate is pushed up an incline from point A to point B as shown in the figure. What is the change in the gravitational potential energy of the crate? C3. Larry's gravitational potential energy is 1870 J as he sits 2.20 m above the ground in a sky diving airplane before it takes off. What is Larry's gravitational potential energy when be begins to jump from the airplane at an altitude of 923 m? C4. A 1500-kg elevator moves upward with constant speed through a vertical distance of 25 m. How much work was done by the tension in the elevator cable? C5. During the construction of a high rise building, 40-kg block is vertically lifted 20 meters from the surface of the earth. To one significant figure, what is the change in the gravitational potential energy of the block? C6. Use the work-energy theorem to find the force required to accelerate an electron (m = 9.11 × 10–31 kg) moving along the x axis from 4.00 × 106 m/s to 1.60 × 107 m/s in a distance of 0.0125 m. D1. A helicopter (m = 3250 kg) is cruising at a speed of 56.9 m/s at an altitude of 185 m. What is the total mechanical energy of the helicopter? D2. A pebble rolls off the roof of Science Hall and falls vertically. Just before it reaches the ground, the pebble's speed is 17 m/s. Neglect air resistance and determine the height of Science Hall. D3. A 2.0-kg projectile is fired with initial velocity components vox = 30 m/s and voy = 40 m/s from a point on the earth's surface. Neglect any effects due to air resistance. What is the kinetic energy of the projectile when it reaches the highest point in its trajectory? D4. Two boxes are connected to each other as shown. The system is released from rest and the 1.00-kg box falls through a distance of 1.00 m. The surface of the table is frictionless. What is the kinetic energy of box B just before it reaches the floor?
3. 3. D5. A roller-coaster car is moving at 20 m/s along a straight horizontal track. What will its speed be after climbing the 15-m hill shown in the figure, if friction is ignored? D6. A 3.0-kg cylinder falls vertically from rest in a very tall, evacuated tube near the surface of the earth. What is its speed after the cylinder has fallen 6.0 m? E1. A bicyclist is traveling at a speed of 20.0 m/s as he approaches the bottom of a hill. He decides to coast up the hill and stops upon reaching the top. Neglecting friction, determine the vertical height of the hill. E2. A skier leaves the top of a slope with an initial speed of 5.0 m/s. Her speed at the bottom of the slope is 13 m/s. What is the height of the slope? E3. A roller coaster starts from rest at the top of an 18-m hill as shown. The car travels to the bottom of the hill and continues up the next hill that is 10.0 m high. How fast is the car moving at the top of the 10.0-m hill, if friction is ignored? E4. An engineer is asked to design a playground slide such that the speed a child reaches at the bottom does not exceed 6.0 m/s. Determine the maximum height that the slide can be. E5. A care package is dropped from rest from a helicopter hovering 25 m above the ground.What is the speed of the package just before it reaches the ground? Neglect air resistance. E6. A block of mass m is released from rest at a height R above a horizontal surface. The acceleration due to gravity is g. The block slides along the inside of a frictionless circular hoop of radius R. What is the speed of the mass at the bottom of the hoop? F1. A physics student shoves a 0.50-kg block from the bottom of a frictionless 30.0° inclined plane. The student performs 4.0 J of work and the block slides a distance s along the incline before it stops. Determine the value of s.
4. 4. F2. The initial velocity of a 4.0-kg box is 11 m/s, due west. After the box slides 4.0 m horizontally, its speed is 1.5 m/s. Determine the magnitude and the direction of the non-conservative force acting on the box as it slides. F3. An automobile approaches a barrier at a speed of 20 m/s along a level road. The driver locks the brakes at a distance of 50 m from the barrier. What minimum coefficient of kinetic friction is required to stop the automobile before it hits the barrier? F4. A 9.0-kg box of oranges slides from rest down a frictionless incline from a height of 5.0 m. A constant frictional force, introduced at point A, brings the block to rest at point B, 19 m to the right of point A. What is the speed of the box just before it reaches point A? F5. Refer to the previous problem F4, what is the coefficient of kinetic friction, mk, of the surface from A to B? F6. The kinetic energy of a car is 8 × 106 J as it travels along a horizontal road. How much power is required to stop the car in 10 s? G1. A 51-kg woman runs up a flight of stairs in 5.0 s. Her net upward displacement is 5.0 m. Approximately, what average power did the woman exert while she was running? G2. What power is needed to lift a 49-kg person a vertical distance of 5.0 m in 20.0 s? G3. An escalator is 30.0 meters long and slants at 30.0° relative to the horizontal. If it moves at 1.00 m/s, at what rate does it do work in lifting a 50.0-kg woman from the bottom to the top of the escalator? G4. How much power is needed to lift a 75-kg student vertically upward at a constant speed of 0.33 m/s? G5. A warehouse worker uses a forklift to raise a crate of pickles on a platform to a height 2.75 m above the floor. The combined mass of the platform and the crate is 207 kg. If the power expended by the forklift is 1440 W, how long does it take to lift the crate? G6. A dam is used to block the passage of a river and to generate electricity. Approximately 5.73 ´ 104 kg of water fall each second through a height of 19.6 m. If 85 % of the gravitational potential energy of the water were converted to electrical energy, how much power would be generated? H1. A motorist driving a 1000-kg car wishes to increase her speed from 20 m/s to 30 m/s in 5 s. Determine the horsepower required to accomplish this increase. Neglect friction. H2. A top fuel dragster with a mass of 500.0 kg starts from rest and completes a quarter mile (402 m) race in a time of 5.0 s. The dragster's final speed is 130 m/s. Neglecting friction, what average power was needed to produce this final speed? H3. A 12.5-kg crate slides along a horizontal frictionless surface at a constant speed of 4.0 m/s. The crate then slides down a frictionless incline and across a second horizontal surface as shown in the figure. What is the kinetic energy of the crate as it slides on the upper surface?
5. 5. H4. Refer to H3 problem. What minimum coefficient of kinetic friction is required to bring the crate to a stop over a distance of 5.0 m along the lower surface? H5. Refer to H3 problem. What is the speed of the crate when it arrives at the lower surface? H6. Refer to H3 problem. What is the kinetic energy of the crate as it slides on the lower surface? I1. A rope exerts a force on a 20.0-kg crate. The crate starts from rest and accelerates upward at 5.00 m/s2 near the surface of the earth. What is the kinetic energy of the crate when it is 4.0 m above the floor? I2. Refer to I1.How much work was done by the force in raising the crate 4.0 m above the floor? I3. A 325-N force accelerates a 50.0-kg crate from rest along a horizontal frictionless surface for a distance of 20.0 m as shown in the figure. What is the final speed of the crate? I4. Refer to I3. How much work is done on the crate? I5. Refer to I3. What coefficient of friction would be required to keep the crate moving at constant speed under the action of the 325-N force? I6. If the crate in the preceding problem were moved at constant speed up a plane inclined at 30 degrees above the horizontal, determine the work done by gravity. Study chapter 6 religiously. You will have a chapter test next week.
6. 6. H4. Refer to H3 problem. What minimum coefficient of kinetic friction is required to bring the crate to a stop over a distance of 5.0 m along the lower surface? H5. Refer to H3 problem. What is the speed of the crate when it arrives at the lower surface? H6. Refer to H3 problem. What is the kinetic energy of the crate as it slides on the lower surface? I1. A rope exerts a force on a 20.0-kg crate. The crate starts from rest and accelerates upward at 5.00 m/s2 near the surface of the earth. What is the kinetic energy of the crate when it is 4.0 m above the floor? I2. Refer to I1.How much work was done by the force in raising the crate 4.0 m above the floor? I3. A 325-N force accelerates a 50.0-kg crate from rest along a horizontal frictionless surface for a distance of 20.0 m as shown in the figure. What is the final speed of the crate? I4. Refer to I3. How much work is done on the crate? I5. Refer to I3. What coefficient of friction would be required to keep the crate moving at constant speed under the action of the 325-N force? I6. If the crate in the preceding problem were moved at constant speed up a plane inclined at 30 degrees above the horizontal, determine the work done by gravity. Study chapter 6 religiously. You will have a chapter test next week.