9.2 Work & Energy Homework - KINETIC, GRAVITATIONAL & SPRING ENERGY

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1 9. Work & Energy Homework - KINETIC, GRAVITATIONAL & SPRING ENERGY KINETIC ENERGY QUESTIONS 9.H Energy.doc 1. A 500 kilogram car is driving at 15 meters/second. Calculate its kinetic energy? How much does the car weigh?. A slow moving car may have more kinetic energy than a fast moving motorcycle. Explain how is this possible? 3. The aircraft carrier Nimitz has a fully loaded mass of kg. It travels a distance of 08 kilometers in 3.5 hours. What is the kinetic energy (in Joules) of the Nimitz? (These are actual numbers) 4. Let s say the Nimitz is traveling at a velocity of 15 m/s and it accelerates up to a velocity of 16 m/s. A) What is the difference in Kinetic Energy of for the two velocities? B) How much Energy must be added in the form of work to accelerate the ship from 15 m/s to 16m/s? 5. What happens to the Kinetic Energy of an object if its mass is doubled and it velocity is not changed? 6. What happens to the Kinetic Energy of an object if its velocity is doubled and its mass is not changed? 7. The dinosaur Tyrannosaurus rex is thought to have had a mass of about 7,000 kilograms. What is the dinosaur s kinetic energy if it walks at 4 kilometers/hour? 8. An average person has a mass of 70 kilograms. How fast must an average person move to have the same kinetic energy as the T. Rex? 9. A baseball leaves a pitcher s hand at a speed of 3 m/s. The mass of the ball is.145 kg. How much work has the pitcher done on the ball? 10. A 4,000 kilogram car is traveling at a velocity of 30 meters/second. It accelerates to 40 meters per second. How much work must the engine do to increase the velocity of the car from 30 meters/second to 40 meters/second? 11. A PRACTICAL PROBLEM - Let s try a question similar to number 3 & 10 with some real numbers and compare the Energy required to accelerate a light car and heavier car the same amount. An average car has a mass of 100 kg (The Physics Factbook). The cars of the smallest mass have a mass of 990 kilograms while the heavier cars have a mass around 000 kilograms. An average gallon of gas has 15 million joules of Energy and costs about $.30 /gallon. A) How many Joules are required to accelerate each vehicle from 0 mph to 30 mph (13.4 m/s) B) By what factor are these values different? C) How many gallons of gas does each require? D) How many $ does each require? SPRING ENERGY QUESTIONS (also known as Elastic Potential Energy) 1. The spring constant for a particular spring is 0 N/m. How much energy is stored in the spring if it stretched.1 meters? 13. If the spring is stretched twice as much will it contain twice as much Spring Energy? 14. If you want to increase the elastic potential energy of a spring by a factor of, by what factor must you increase the stretch of the spring? 15. If you want to increase the elastic potential energy of a spring by a factor of 3, by what factor must you increase the stretch of the spring? GRAVITIATIONAL POTENTIAL ENERGY QUESTIONS 16. An object with a mass of 10 kilograms is 5 meters above the ground. How much GPE does it have? 17. A refrigerator (100 kg) is lifted from the 30 th floor to the 34 th floor of a building (each floor is 3 meters). What is the increase in GPE of the refrigerator? 18. How much work must be done to move the refrigerator from the 4 th floor to the 8 th floor?

2 19. The space shuttle has a mass of 11,100 kg. It flies to a height of about 00 miles (31,900 meters) above the surface of Earth. What is the change in GPE between the lift-off and orbit elevation? ENERGY CONVERSION MACHINES/ NATURE Many machines were invented to convert Energy from one form to another such as an electric heater. It turns Electric Energy into Heat, at least that s the idea anyway. Of course some of the energy is converted into light as well and therefore useless as far as a heater goes. Nature has created its own machines for converting energy from one form to another. Fill in the chart with machines (manmade and natural) that convert between the various forms of energy. (This sheet may be too small, if so recreate on a spreadsheet and complete)

3 9.3 LAW OF CONSERVATION OF ENERGY Work & Energy Homework - ENERGY TRANSFORMATIONS WITH NO WORK OR FRICTIONAL LOSSES Stragety for Working Energy Problems 1. Select the system and its starting (E 1) and ending state (E ). Write the Law of Conservation of Energy (E 1 = E ). Write the Equation for each state, include all types of Energy (use the initials for the forms of energy) E1 = E { KE1 + GPE1 + EPE1 } = { KE + GPE + EPE } 3. Cross out values that are equal to zero to simplify the equation. 4. Substitute in the equations for the remaining forms of energy mv mgh kx 1 mv mgh kx 5. Solve the remaining equation for the desired variable. 6. Plug and Chug Law of Conservation of Energy Use the Law of Conservation of Energy to solve the following problems. 1. An elevator has an unknown mass. The elevator is at the top floor of the Sears Tower that is 440 meters high. If the cable holding the elevator were to snap, what velocity would it have when it hits the ground floor? (We must assume no friction is present). A general form of the above question An object with a mass of m starts at rest a height h above the ground. At what velocity will it hit the ground? 3. Question is an example of Energy being converted to Energy. 4. A baseball with a mass.145 kg is thrown with a velocity 10 m/s straight down. If the ball starts from a height of 0 meters, how fast is the ball going when it hits the ground? 5. A baseball with a mass.145 kg is thrown with a velocity 10 m/s straight up. If the ball starts from a height of 0 meters, how fast is the ball going when it hits the ground? 6. A baseball with a mass.145 kg is thrown with a velocity 10 m/s 45 above the horizontal. If the ball starts from a height of 0 meters, how fast is the ball going when it hits the ground? 7. A baseball with a mass.145 kg is thrown with a velocity 10 m/s 45 below the horizontal. If the ball starts from a height of 0 meters, how fast is the ball going when it hits the ground? 8. Questions 3-7 are examples of - being converted to. 9. A ball is thrown from the ground (assume it leaves the person s hand at zero elevation) straight up with a velocity of 15 m/s. What is the greatest height the ball reaches? 10. A ball is thrown from the ground (assume it leaves the person s hand at zero elevation) straight up with a velocity of v. What is the greatest height the ball reaches? 11. Questions 9&10 are examples of - being converted to. 1. A baseball (m =.145 kg) at rest is dropped from a height of 10 meters onto a spring with a spring constant of 5N/m. How much will the spring be compressed? 13. An object with a mass of m at rest is dropped from a height of h onto a spring with a spring constant of k. How much will the spring be compressed? 14. Questions 1&13 are examples of - being converted to. 15. A baseball traveling at m/s straight down is at a height of 10 meters and falls onto a spring with a spring with a spring constant of 5N/m. How much will the spring be compressed? 16. A baseball traveling at m/s straight up is at a height of 10 meters and falls onto a spring with a spring constant of 5N/m. How much will the spring be compressed? 17. An object traveling v straight down is at a height of m and falls onto a spring with a spring constant of k. How much will the spring be compressed? 18. Questions 15&17 are examples of - being converted to.

4 Practical Problems Employing the Law of Conservation of Energy Use the Law of Conservation of Energy to solve the following problems. 19. A roller coaster has a max height of 40 meters above its lowest point (about 10 feet) assuming there is no friction, what is the velocity of the roller coaster at the bottom of the hill? 0. If the roller coaster starts at a height of 40 meters and a velocity of zero, how high a hill will the roller coaster be able to climb? 1. If the roller coaster started from twice as high, would it be going twice as fast at the bottom of the hill? Calculate the factor by which velocity at the bottom of the hill is increased if the starting height is increased by a factor of.. Tarzan finds himself stuck on the opposite side of a river filled with hungry crocodiles. To make it up to Jane there is a vine upon which he can swing up to her. The vine is 10 meters long and starts out hanging straight down as shown by the dashed line. To swing up to Jane, Tarzan runs and jumps onto the vine. He must swing the vine through an angle ( θ ) of 40 to make it up to the other side. How fast must he be going to make it up to Jane. (Assume he hits the rope with a horizontal velocity) 3. The launch mechanism of a spring gun has a spring that can be compressed.1 meters. The bullet (0 grams) reaches a maximum height of 0 meters. (A) Calculate the spring constant of the Spring. (B) Calculate the velocity of the bullet as it leaves the spring. 4. The length of a pinball machine tilted surface is 1. meters and is angled at 10. If the spring can be compressed by a distance of 5 cm, what must the spring constant be so that the ball will make it to the top of the sloped surface?

5 5. A ballistic pendulum is a simple device used to indirectly measure the velocity of a bullet. The pendulum is made of a substance that allows the bullet to become imbedded in it. The pendulum catches the bullet and the pendulum is moved and swung upwards turning the kinetic energy into gravitational potential energy. Given that the mass of the bullet is m, the mass of the pendulum is M and the pendulum is lifted a distance y; derive and equation that will give the velocity v of the bullet as a function of the given values. THE BALLISTIC PENDULUM Ballistic Pendulum at Rest - a mass M hangs from two lines. Ballistic Pendulum Just Prior to Bullet Strike - a mass M hangs from two lines is about to be struck by a bullet of mass m traveling horizontally with a velocity v. The combined mass will swing as shown Ballistic Pendulum at Maximum Height the combined mass (M +m) swings to its maximum height above the rest position y. 6. You are asked to design a ballistic pendulum for a gun that fires bullets from 600 ft/s to 800 ft/s. The masses of the bullets range from 45 grams to 47 grams. The ballistic pendulum must not be lifted more than half a meter. What should its mass be? 7. You are asked to design a ballistic pendulum for a gun that fires bullets from 600 ft/s to 800 ft/s. The masses of the bullets range from 45 grams to 47 grams. The ballistic pendulum pivot lines must not be rotate more than 45. What should its mass be? How long should the support lines be? 8. What is the Lowest Energy Theorem?