Set 7 - Energy Explanations PDF

SET 7 – ENERGY (EXPLANATIONS) There are 53 questions in Set 7. DEFINITIONS WORK, ENERGY 1. The energy that a body has because of its position (e.g., in a gravitational field). This describes ____ a. Work b. Power c...

SET 7 – ENERGY (EXPLANATIONS) There are 53 questions in Set 7. DEFINITIONS WORK, ENERGY 1. The energy that a body has because of its position (e.g., in a gravitational field). This describes ____ a. Work b. Power c. Energy d. POTENTIAL ENERGY e. Kinetic energy f. Work-energy theorem g. Conservation of energy h. Machine i. Conservation of energy for machines j. Efficiency Explanation:. Potential energy is defined as the energy that a body has by virtue of its position (e.g., in a field).. The potential energy can be gravitational potential energy (in a gravitational field), or electrical potential energy (in an electrical field), or magnetic potential energy (in a magnetic field), or elastic potential energy (in an elastic strain field). 2. Force multiplied by distance moved by the object upon which the force is acting. This describes ____ a. WORK b. Power 232 c. Energy d. Potential energy e. Kinetic energy f. Work-energy theorem g. Conservation of energy h. Machine i. Conservation of energy for machines j. Efficiency Explanation:. If a force F acts on an object, and moves the object through a distance d (in the direction of the force), then the work done Work = force * distance.. 3. Useful work output divided by total energy (or work) input into a machine. This describes ____ a. Work b. Power c. Energy d. Potential energy e. Kinetic energy f. Work-energy theorem g. Conservation of energy h. Machine i. Conservation of energy for machines j. EFFICIENCY Explanation:. The efficiency of a machine is defined as the useful work output (by the machine) divided by the total energy (or work) input into the machine. 233  FORMULAE WORK 4. For a fixed distance-travelled (in the direction of the applied force), if the force that is applied to an object is increased by 2x, then the work that is done by the force (on the object) will ___ a. Decrease by 2x b. Stays the same c. INCREASE BY 2X d. Increase by 4x Explanation:. If a force acts on an object, and moves the object through a distance (that is in the direction of the application of the force), then the work done = force * distance.. W = F*d, where W is the work done, F is the applied force, and d is the distance moved.. W = F*d.. Therefore, the work done is directly proportional to the applied force.. Consequently, for a fixed distance-travelled (in the direction of the applied force), if the force that is applied to an object is increased by 2x, then the work that is done by the force (on the object) will increase by 2x. 5. For a fixed distance-travelled (in the direction of the applied force), and the work that is done by the force (on an object) is increased, then the force that was applied to the object must have been a. INCREASED b. Decreased 234 c. the same d. Depends on gravity Explanation:. If a force acts on an object, and moves the object through a distance (that is in the direction of the application of the force), then the work done = force * distance.. W = F*d, where W is the work done, F is the applied force, and d is the distance moved.. W = F*d.. Therefore, the work done is directly proportional to the applied force.. Consequently, for a fixed distance-travelled (in the direction of the applied force), if the work that is done by the force (on an object) is increased, then the force that was applied to the object must have been increased. 6. For a fixed distance-travelled (in the direction of the applied force), and the work that is done by the force (on an object) is decreased by 3x, then the force that was applied to the object must have been___ a. DECREASED BY 3X b. the same c. Increased by 3x d. Increased by 9x Explanation:. If a force acts on an object, and moves the object through a distance (that is in the direction of the application of the force), then the work done = force * distance.. W = F*d, where W is the work done, F is the applied force, and d is 235 the distance moved.. W = F*d.. Therefore, the work done is directly proportional to the applied force.. Consequently, for a fixed distance-travelled (in the direction of the applied force), if the work that is done by the force (on an object) is decreased by 3x, then the force that was applied to the object must have been decreased by 3x. 7. If a fixed-force is applied to an object, and the distance-travelled by the object (in the direction of the applied force) is decreased by 2x, then the work that is done by the force (on the object) will a. DECREASE BY 2X b. Stays the same c. Increase by 2x d. Increase by 4x Explanation:. If a force acts on an object, and moves the object through a distance (that is in the direction of the application of the force), then the work done = force * distance.. W = F*d, where W is the work done, F is the applied force, and d is the distance moved.. W = F*d.. Therefore, the work done is directly proportional to the distance travelled.. Consequently, if a fixed-force is applied to an object, and the distance-travelled by the object (in the direction of the applied force) 236 is decreased by 2x, then the work that is done by the force (on the object) will decrease by 2x. 8. For a fixed amount of work done (by a force on an object), if the force that is applied to an object is increased by 3x, then the distance-travelled by the object (in the direction of the applied force) must have ___ a. DECREASED BY 3X b. Stayed the same c. Increased by 3x d. Increased by 9x Explanation:. If a force acts on an object, and moves the object through a distance (that is in the direction of the application of the force), then the work done = force * distance.. W = F*d, where W is the work done, F is the applied force, and d is the distance moved.. W = F*d.. Therefore, for a fixed amount of work done, the required force is inversely proportional to the distance travelled.. Consequently, for a fixed amount of work done (by a force on an object), if the force that is applied to an object is increased by 3x, then the distance-travelled by the object (in the direction of the applied force) must have decreased by 3x. 9. For a fixed amount of work done (by a force on an object), if the distance-travelled by the object (in the direction of the applied force) increases by 2x, then the force that is applied to the object must be___ a. DECREASED BY 2X 237 b. the same c. Increased by 2x d. Increased by 4x Explanation:. If a force acts on an object, and moves the object through a distance (that is in the direction of the application of the force), then the work done = force * distance.. W = F*d, where W is the work done, F is the applied force, and d is the distance moved.. W = F*d.. Therefore, for a fixed amount of work done, the required force is inversely proportional to the distance travelled.. Consequently, for a fixed amount of work done (by a force on an object), if the distance-travelled by the object (in the direction of the applied force) increases by 2x, then the force that is applied to the object must be decreased by 2x. POWER 10. When work is done by a force over a period of time, the power can be calculated by Power = a. WORK / TIME b. Work * time c. 0.5* Work / time / time d. change in work / time e. 0.5 * Work Explanation:. Power is defined as the time-rate of work done. 238. In other words, power = work /time.. P = W/t, where P is the power, W is the work done, and t is the time- duration. 11. For a fixed time-duration, if the power that is applied to an object decreased by 2x, the work done will have___ a. DECREASED BY 2X b. Stays the same c. Increased by 2x d. Increased by 4x Explanation:. Power is defined as the time-rate of work done.. In other words, power = work /time.. P = W/t, where P is the power, W is the work done, and t is the time- duration.. Therefore, if the time-duration is fixed, the power is directly proportional to the work done.. Consequently, for a fixed time-duration, if the power that is applied to an object decreased by 2x, the work done will have decreased by 2x. 12. For a fixed time-duration, and the work that is done on the object is increased by 3x, the power that was applied to the object must have been___ a. Decreased by 3x b. the same c. INCREASED BY 3X d. Increased by 9x 239 Explanation:. Power is defined as the time-rate of work done.. In other words, power = work /time.. P = W/t, where P is the power, W is the work done, and t is the time- duration.. Therefore, if the time-duration is fixed, the power is directly proportional to the work done.. Consequently, for a fixed time-duration, if the work that is done on an object is increased by 3x, the power that was applied to the object must have been increased by 3x. 13. If a fixed rate of power is applied to an object, and the time- duration of the application of the power to the object is increased by 2x, the work done will a. Decrease by 2x b. Stays the same c. INCREASE BY 2X d. Increase by 4x Explanation:. Power is defined as the time-rate of work done.. In other words, power = work /time.. P = W/t, where P is the power, W is the work done, and t is the time- duration.. Multiplying both sides of this equation by t, we obtain the following equation, W = P*t. 240. Therefore, if the power is fixed, the work done is directly proportional to the time-duration.. Consequently, if a fixed rate of power is applied to an object, and the time-duration of the application of the power to the object is increased by 2x, the work done will increase by 2x. 14. If a fixed rate of power is applied to an object, and the work that is done on the object is increased, then the time-duration of the application of the power to the object must have been a. INCREASED b. Decreased c. the same d. Depends on gravity Explanation:. Power is defined as the time-rate of work done.. In other words, power = work /time.. P = W/t, where P is the power, W is the work done, and t is the time- duration.. Multiplying both sides of this equation by t, we obtain the following equation, W = P*t.. Therefore, if the power is fixed, the work done is directly proportional to the time-duration.. Consequently, if a fixed rate of power is applied to an object, and the work that is done on the object is increased, then the time-duration of the application of the power to the object must have been increased. 241 15. If a fixed rate of power is applied to an object, and the work that is done on the object is decreased by 3x, then the time-duration of the application of the power to the object must have been___ a. DECREASED BY 3X b. the same c. Increased by 3x d. Increased by 9x Explanation:. Power is defined as the time-rate of work done.. In other words, power = work /time.. P = W/t, where P is the power, W is the work done, and t is the time- duration.. Multiplying both sides of this equation by t, we obtain the following equation, W = P*t.. Therefore, if the power is fixed, the work done is directly proportional to the time-duration.. Consequently, if a fixed rate of power is applied to an object, and the work that is done on the object is decreased by 3x, then the time- duration of the application of the power to the object must have been decreased by 3x. 16. In order to perform a fixed amount of work (on an object), if the power that is applied to the object decreases by 2x, then the time- duration of the application of the power to the object must have ___ a. Decreased by 2x b. Stays the same c. INCREASED BY 2X d. Increased by 4x 242 Explanation:. Power is defined as the time-rate of work done.. In other words, power = work /time.. P = W/t, where P is the power, W is the work done, and t is the time- duration.. Therefore, if the work that is done is fixed, the power is inversely proportional to the time-duration.. Consequently, in order to perform a fixed amount of work (on an object), if the power that is applied to the object decreases by 2x, then the time-duration of the application of the power to the object must have increased by 2x. 17. In order to perform a fixed amount of work (on an object), if the time-duration of the application of power to the object increases by 3x, then the power that is applied to the object must be___ a. DECREASED BY 3X b. the same c. Increased by 3x d. Increased by 9x e. Increased by 4x Explanation:. Power is defined as the time-rate of work done.. In other words, power = work /time.. P = W/t, where P is the power, W is the work done, and t is the time- duration.. Therefore, if the work that is done is fixed, the power is inversely 243 proportional to the time-duration.. Consequently, in order to perform a fixed amount of work (on an object), if the time-duration of the application of power to the object increases by 3x, then the power that is applied to the object must be decreased by 3x. POTENTIAL ENERGY 18. An object with a mass “m” is held up at a height “h” in a gravitational field that is characterized by an acceleration-due-to- gravity of “g”. If m and g are fixed, and the height (at which the object is held above the ground) increases, then the gravitational potential-energy must a. decrease b. INCREASE c. Stay the same d. Depends on gravity Explanation:. The gravitational potential energy of an object is given by PE = m*g*h, where PE is the potential energy, m is the mass, g is the acceleration due to gravity, and h is the height of the object above the earth’s surface.. Therefore, the gravitational potential energy is directly proportional to the height of the object above the earth’s surface.. Consequently, if m and g are fixed, and the height (at which the object is held above the ground) increases, then the gravitational potential-energy must increase. 19. An object with a mass “m” is held up at a height “h” in a gravitational field that is characterized by an acceleration-due-to- gravity of “g”. If m and g are fixed, and the height (at which the 244 object is held above the ground) is decreased by 3x, then the gravitational potential-energy must___ a. increase by 3x b. Stay the same c. DECREASE BY 3X d. Increase by 9x Explanation:. The gravitational potential energy of an object is given by PE = m*g*h, where PE is the potential energy, m is the mass, g is the acceleration due to gravity, and h is the height of the object above the earth’s surface.. Therefore, the gravitational potential energy is directly proportional to the height of the object above the earth’s surface.. Consequently, if m and g are fixed, and the height (at which the object is held above the ground) is decreased by 3x, then the gravitational potential-energy must decrease by 3x.. 20. An object with a mass “m” is held up at a height “h” in a gravitational field that is characterized by an acceleration-due-to- gravity of “g”. If m and g are fixed, and the gravitational potential- energy is decreased by 2x, then the height (at which the object is held above the ground) must___ a. increase by 2x b. Stay the same c. DECREASE BY 2X d. Increase by 4x Explanation:. The gravitational potential energy of an object is given by PE = 245 m*g*h, where PE is the potential energy, m is the mass, g is the acceleration due to gravity, and h is the height of the object above the earth’s surface.. Therefore, the gravitational potential energy is directly proportional to the height of the object above the earth’s surface.. Consequently, if m and g are fixed, and the gravitational potential- energy is decreased by 2x, then the height (at which the object is held above the ground) must decrease by 2x. 21. An object with a mass “m” is held up at a height “h” in a gravitational field that is characterized by an acceleration-due-to- gravity of “g”. If g and h are fixed, and the mass of the object is increased by 3x, then the gravitational potential-energy must___ a. INCREASE BY 3X b. Stay the same c. decrease by 3x d. Increase by 9x Explanation:. The gravitational potential energy of an object is given by PE = m*g*h, where PE is the potential energy, m is the mass, g is the acceleration due to gravity, and h is the height of the object above the earth’s surface.. Therefore, the gravitational potential energy is directly proportional to the mass of the object.. Consequently, if g and h are fixed, and the mass of the object is increased by 3x, then the gravitational potential-energy must increase by 3x. 22. An object with a mass “m” is held up at a height “h” in a gravitational field that is characterized by an acceleration-due-to- 246 gravity of “g”. If g and h are fixed, and the gravitational potential- energy is increased by 2x, then the mass of the object must have___ a. INCREASED BY 2X b. Stay the same c. decreased by 2x d. Increased by 4x Explanation:. The gravitational potential energy of an object is given by PE = m*g*h, where PE is the potential energy, m is the mass, g is the acceleration due to gravity, and h is the height of the object above the earth’s surface.. Therefore, the gravitational potential energy is directly proportional to the mass of the object.. Consequently, if g and h are fixed, and the gravitational potential- energy is increased by 2x, then the mass of the object must have increased by 2x. 23. An object with a mass “m” is held up at a height “h” in a gravitational field that is characterized by an acceleration-due-to- gravity of “g”. If m and h are fixed, and g increases, then the gravitational potential-energy must a. decrease b. INCREASE c. Stay the same d. Depends on gravity Explanation:. The gravitational potential energy of an object is given by PE = m*g*h, where PE is the potential energy, m is the mass, g is the acceleration due to gravity, and h is the height of the object above the earth’s surface. 247. Therefore, the gravitational potential energy is directly proportional to the acceleration due to gravity.. Consequently, if m and h are fixed, and g increases, then the gravitational potential-energy must increase. 24. An object with a mass “m” is held up at a height “h” in a gravitational field that is characterized by an acceleration-due-to- gravity of “g”. If m and h are fixed, and g is decreased by 3x, then the gravitational potential-energy must___ a. increase by 3x b. Stay the same c. DECREASE BY 3X d. Increase by 9x Explanation:. The gravitational potential energy of an object is given by PE = m*g*h, where PE is the potential energy, m is the mass, g is the acceleration due to gravity, and h is the height of the object above the earth’s surface.. Therefore, the gravitational potential energy is directly proportional to the acceleration due to gravity.. Consequently, if m and h are fixed, and g decreases by 3x, then the gravitational potential-energy must decrease by 3x. 25. An object with a mass “m” is held up at a height “h” in a gravitational field that is characterized by an acceleration-due-to- gravity of “g”. If m and h are fixed, and the gravitational potential- energy is decreased by 2x, then g must have___ a. increased by 2x b. Stay the same 248 c. DECREASED BY 2X d. Increased by 4x Explanation:. The gravitational potential energy of an object is given by PE = m*g*h, where PE is the potential energy, m is the mass, g is the acceleration due to gravity, and h is the height of the object above the earth’s surface.. Therefore, the gravitational potential energy is directly proportional to the acceleration due to gravity.. Consequently, if m and h are fixed, and the gravitational potential- energy has decreased by 2x, then g must have decreased by 2x. KINETIC ENERGY 26. An object with a mass “m” is traveling with a velocity “v”. If m is fixed, and the velocity is increased by 2x, then the kinetic energy must___ a. INCREASE BY 4X b. Stay the same c. decrease by 2x d. Increase by 2x Explanation:. The kinetic energy of a moving object is given by KE = 0.5*m*v*v, where KE is the kinetic energy of the object, m is the mass of the object, and v is the velocity of the object.. Therefore, the kinetic energy is proportional to the velocity-squared. Consequently, if m is fixed, and the velocity is increased by 2x, then the kinetic energy must increase by 4x. 249 27. An object with a mass “m” is traveling with a velocity “v”. If m is fixed, and the kinetic energy increases, then the velocity must a. decrease b. INCREASE c. Stay the same d. Depends on gravity Explanation:. The kinetic energy of a moving object is given by KE = 0.5*m*v*v, where KE is the kinetic energy of the object, m is the mass of the object, and v is the velocity of the object.. Therefore, the kinetic energy is proportional to the velocity-squared. Consequently, if m is fixed, and the kinetic energy increases, then the velocity must increase. 28. An object with a mass “m” is traveling with a velocity “v”. If m is fixed, and the kinetic energy is decreased by 9x, then the velocity must___ a. increase by 3x b. Stay the same c. DECREASE BY 3X d. Increase by 9x Explanation:. The kinetic energy of a moving object is given by KE = 0.5*m*v*v, where KE is the kinetic energy of the object, m is the mass of the object, and v is the velocity of the object.. Therefore, the kinetic energy is proportional to the velocity-squared. Consequently, if m is fixed, and the kinetic energy is decreased by 9x, then the velocity must decrease by 3x. 250 29. An object with a mass “m” is traveling with a velocity “v”. If the velocity is fixed, and the mass of the object is decreased by 2x, then the kinetic energy must___ a. increase by 2x b. Stay the same c. DECREASE BY 2X d. Increase by 4x Explanation:. The kinetic energy of a moving object is given by KE = 0.5*m*v*v, where KE is the kinetic energy of the object, m is the mass of the object, and v is the velocity of the object.. Therefore, the kinetic energy is proportional to the mass.. Consequently, if the velocity is fixed, and the mass of the object has decreased by 2x, then the kinetic energy must decrease by 2x. 30. An object with a mass “m” is traveling with a velocity “v”. If the velocity is fixed, and the kinetic energy is increased by 3x, then the mass of the object must have___ a. INCREASED BY 3X b. Stay the same c. decreased by 3x d. Increased by 9x Explanation:. The kinetic energy of a moving object is given by KE = 0.5*m*v*v, where KE is the kinetic energy of the object, m is the mass of the object, and v is the velocity of the object.. Therefore, the kinetic energy is proportional to the mass. 251. Consequently, if the velocity is fixed, and the kinetic energy has increased by 3x, then the mass of the object must have increased by 3x. MACHINE WORK 31. A machine is configured so that work is input into the machine by a force F1 that is used to move a lever through a distance d1. The machine converts this into output work by moving an output lever through a distance d2, with an output force of F2. If the values of F1 and d1 are held constant, and the value of F2 is decreased, then the value of d2 a. INCREASES b. Decreases c. Stays the same d. Depends on gravity Explanation:. The work input into the machine is given by W1 = F1*d1. The work output by the machine is given by W2 = F2*d2. In the absence of friction, the work output equals the work input.. Hence, F2*d2 = F1*d1. Dividing both sides of the equation by d2, we obtain F2 = F1*d1/d2. Therefore, F2 is inversely proportional to d2. Consequently, if the values of F1 and d1 are held constant, and the value of F2 is decreased, then the value of d2 increases. 32. A machine is configured so that work is input into the machine by a force F1 that is used to move a lever through a distance d1. The machine converts this into output work by moving an output lever through a distance d2, with an output force of F2. If the values of F1 and d1 are held constant, and the value of F2 is increased by 3x, then the value of d2 a. DECREASES BY 3X 252 b. Stays the same c. Increases by 3x d. Increases by 9x Explanation:. The work input into the machine is given by W1 = F1*d1. The work output by the machine is given by W2 = F2*d2. In the absence of friction, the work output equals the work input.. Hence, F2*d2 = F1*d1. Dividing both sides of the equation by d2, we obtain F2 = F1*d1/d2. Therefore, F2 is inversely proportional to d2. Consequently, if the values of F1 and d1 are held constant, and the value of F2 is increased by 3x, then the value of d2 decreases by 3x. 33. A machine is configured so that work is input into the machine by a force F1 that is used to move a lever through a distance d1. The machine converts this into output work by moving an output lever through a distance d2, with an output force of F2. If the values of F1 and d1 are held constant, and the value of d2 is increased by 2x, then the value of F2 a. DECREASES BY 2X b. Stays the same c. Increases by 2x d. Increases by 4x Explanation:. The work input into the machine is given by W1 = F1*d1. The work output by the machine is given by W2 = F2*d2. In the absence of friction, the work output equals the work input.. Hence, F2*d2 = F1*d1. Dividing both sides of the equation by d2, we obtain F2 = F1*d1/d2. Therefore, F2 is inversely proportional to d2. Consequently, if the values of F1 and d1 are held constant, and the value of d2 is increased by 2x, then the value of F2 decreases by 2x. 253 34. A machine is configured so that work is input into the machine by a force F1 that is used to move a lever through a distance d1. The machine converts this into output work by moving an output lever through a distance d2, with an output force of F2. If the values of F2 and d2 are held constant, and the value of F1 is decreased by 3x, then the value of d1 a. Decreases by 3x b. Stays the same c. INCREASES BY 3X d. Increases by 9x Explanation:. The work input into the machine is given by W1 = F1*d1. The work output by the machine is given by W2 = F2*d2. In the absence of friction, the work output equals the work input.. Hence, F2*d2 = F1*d1. Dividing both sides of the equation by d1, we obtain F1 = F2*d2/d1. Therefore, F1 is inversely proportional to d1. Consequently, if the values of F2 and d2 are held constant, and the value of F1 is decreased by 3x, then the value of d1 increases by 3x. 35. A machine is configured so that work is input into the machine by a force F1 that is used to move a lever through a distance d1. The machine converts this into output work by moving an output lever through a distance d2, with an output force of F2. If the values of F2 and d2 are held constant, and the value of d1 is decreased by 2x, then the value of F1 a. Decreases by 2x b. Stays the same c. INCREASES BY 2X d. Increases by 4x 254 Explanation:. The work input into the machine is given by W1 = F1*d1. The work output by the machine is given by W2 = F2*d2. In the absence of friction, the work output equals the work input.. Hence, F2*d2 = F1*d1. Dividing both sides of the equation by d1, we obtain F1 = F2*d2/d1. Therefore, F1 is inversely proportional to d1. Consequently, if the values of F2 and d2 are held constant, and the value of d1 is decreased by 2x, then the value of F1 increases by 2x. EFFICIENCY 36. Given a certain amount of useful work output for a given work input (to a machine), the efficiency of a machine or a process is given by Efficiency = a. USEFUL WORK OUTPUT / WORK INPUT b. Useful work output * work input c. 0.5* Useful work output / work input / work input d. change in Useful work output / work input e. 0.5 * Useful work output Explanation:. The efficiency of a machine is defined as the useful work output/work input.. Eff = Wo/Wi, where Eff is the efficiency, Wo is the useful work output, and Wi is the work input.. 37. For a fixed work input (to a machine), if the efficiency of the machine decreased by 2x, the useful work output will___ a. DECREASE BY 2X 255 b. Stay the same c. Increase by 2x d. Increase by 4x Explanation:. The efficiency of a machine is defined as the useful work output/work input.. Eff = Wo/Wi, where Eff is the efficiency, Wo is the useful work output, and Wi is the work input.. Therefore, the work output is directly proportional to the efficiency of the machine.. Consequently, for a fixed work input (to a machine), if the efficiency of the machine decreased by 2x, the useful work output will decrease by 2x. 38. For a fixed work input (to a machine), if the useful work output of the machine is increased by 3x, then the efficiency of the machine must have been___ a. Decreased by 3x b. the same c. INCREASED BY 3X d. Increased by 9x Explanation:. The efficiency of a machine is defined as the useful work output/work input.. Eff = Wo/Wi, where Eff is the efficiency, Wo is the useful work output, and Wi is the work input.. Therefore, the work output is directly proportional to the efficiency of 256 the machine.. Consequently, for a fixed work input (to a machine), if the useful work output of the machine is increased by 3x, then the efficiency of the machine must have been increased by 3x. 39. If the efficiency of a machine is fixed, and the work input to the machine is increased by 2x, the useful work output by the machine will a. Decrease by 2x b. Stay the same c. INCREASE BY 2X d. Increase by 4x Explanation:. The efficiency of a machine is defined as the useful work output/work input.. Eff = Wo/Wi, where Eff is the efficiency, Wo is the useful work output, and Wi is the work input.. Therefore, the work output is directly proportional to the work input.. Consequently, if the efficiency of a machine is fixed, and the work input to the machine is increased by 2x, the useful work output by the machine will increase by 2x. 40. If the efficiency of a machine is fixed, and the useful work output of the machine is increased, then the work input to the machine must have been a. INCREASED b. Decreased c. the same d. Depends on gravity 257 Explanation:. The efficiency of a machine is defined as the useful work output/work input.. Eff = Wo/Wi, where Eff is the efficiency, Wo is the useful work output, and Wi is the work input.. Therefore, the work output is directly proportional to the work input.. Consequently, if the efficiency of a machine is fixed, and the useful work output of the machine is increased, then the work input to the machine must have been increased. 41. If the efficiency of a machine is fixed, and the useful work output of the machine is decreased by 3x, then the work input to the machine must have been___ a. DECREASED BY 3X b. the same c. Increased by 3x d. Increased by 9x Explanation:. The efficiency of a machine is defined as the useful work output/work input.. Eff = Wo/Wi, where Eff is the efficiency, Wo is the useful work output, and Wi is the work input.. Therefore, the work output is directly proportional to the work input.. Consequently, if the efficiency of a machine is fixed, and the useful work output of the machine is decreased by 3x, then the work input to the machine must have been decreased by 3x. 258 42. In order for a machine to perform a fixed amount of useful work (output), if the efficiency of the machine is decreased by 2x, then the work input to the machine must have ___ a. Decreased by 2x b. Stay the same c. INCREASED BY 2X d. Increased by 4x Explanation:. The efficiency of a machine is defined as the useful work output/work input.. Eff = Wo/Wi, where Eff is the efficiency, Wo is the useful work output, and Wi is the work input.. Therefore, the efficiency is inversely proportional to the work input.. Consequently, in order for a machine to perform a fixed amount of useful work (output), if the efficiency of the machine is decreased by 2x, then the work input to the machine must have increased by 2x. 43. In order for a machine to perform a fixed amount of useful work (output), if the required work input to the machine increases by 3x, then the efficiency of the machine must have___ a. DECREASED BY 3X b. the same c. Increased by 3x d. Increased by 9x Explanation:. The efficiency of a machine is defined as the useful work output/work input. 259. Eff = Wo/Wi, where Eff is the efficiency, Wo is the useful work output, and Wi is the work input.. Therefore, the efficiency is inversely proportional to the work input.. Consequently, in order for a machine to perform a fixed amount of useful work (output), if the required work input to the machine increases by 3x, then the efficiency of the machine must have decreased by 3x. CONCEPTS 44. If you double the speed of a car, its acceleration necessarily ___ its original value a. Increases to 2x b. Decreases to 2x c. Increases to 4x d. Decreases to 4x e. NONE OF THE ABOVE Explanation: 260. Doubling the speed of a car does not necessarily change the acceleration of the car.. The speed can be doubled while maintaining a constant acceleration, or a decreased acceleration, or an increased acceleration.. Therefore, the correct answer is: none of the above. 45. If you double the speed of a car, the magnitude of its velocity necessarily ___ its original value a. INCREASES TO 2X b. Decreases to 2x c. Increases to 4x d. Decreases to 4x e. None of the above 261 Explanation:. The magnitude of the velocity of an object is the same as the speed of the object.. Therefore, if you double the speed of a car, the magnitude of its velocity necessarily increases to 2x its original value. 46. If you increase the speed of a car to 3x its original speed, then its kinetic energy necessarily ___ its original value a. Increases to 3x b. Decreases to 3x c. INCREASES TO 9X d. Decreases to 9x e. None of the above Explanation: 262. The kinetic energy of a moving object is given by KE = 0.5*m*v*v, where KE is the kinetic energy of the object, m is the mass of the object, and v is the velocity of the object.. Therefore, the kinetic energy is proportional to the velocity-squared. Consequently, if you increase the speed of a car to 3x its original speed, then its kinetic energy necessarily increases to 9x its original value.. 47. If you double the mass of a car, its acceleration necessarily ___ its original value a. Increases to 2x b. Decreases to 2x c. Increases to 4x d. Decreases to 4x e. NONE OF THE ABOVE Explanation: 263. Doubling the mass of a car does not necessarily change the acceleration of the car.. In principle (though maybe not in practice), the mass can be doubled while maintaining a constant acceleration, or a decreased acceleration, or an increased acceleration.. Therefore, the correct answer is: none of the above. 48. If you double the mass of a car, the magnitude of its velocity necessarily ___ its original value a. Increases to 2x b. Decreases to 2x c. Increases to 4x d. Decreases to 4x E. NONE OF THE ABOVE Explanation: 264. Doubling the mass of a car does not necessarily change the velocity of the car.. In principle (though maybe not in practice), the mass can be doubled while maintaining a constant velocity, or a decreasing velocity, or an increasing velocity.. Therefore, the correct answer is: none of the above. 49. Given a fixed velocity, if you increase the mass of a car to 3x its original mass, then its kinetic energy necessarily ___ its original value a. INCREASES TO 3X b. Decreases to 3x c. Increases to 9x d. Decreases to 9x e. None of the above Explanation: 265. The kinetic energy of a moving object is given by KE = 0.5*m*v*v, where KE is the kinetic energy of the object, m is the mass of the object, and v is the velocity of the object.. Therefore, the kinetic energy is proportional to the mass of the object.. Consequently, given a fixed velocity, if you increase the mass of a car to 3x its original mass, then its kinetic energy necessarily increases to 3x its original value. 50. An object has kinetic energy.. This means that it also necessarily has a. A force acting on it b. Potential energy c. Acceleration d. MOMENTUM 266 Explanation:. The kinetic energy of a moving object is given by KE = 0.5*m*v*v, where KE is the kinetic energy of the object, m is the mass of the object, and v is the velocity of the object.. Therefore, if the object has kinetic energy, it must have mass, and velocity.. It does not need to have a force currently acting on it.. It does not need to have gravitational potential energy.. And it does not need to have a current acceleration.. However, since it has mass and velocity, it necessarily has momentum (since momentum = mass * velocity). 51. An object has gravitational potential energy.. 267 This means that it also necessarily has a. MASS b. momentum c. Kinetic energy d. Momentum and kinetic energy Explanation:. The gravitational potential energy is given by PE = m*g*h, where PE is the potential energy, m is the mass, g is the acceleration due to gravity, and h is the height of the object above the earth’s surface.. If the object has gravitational potential energy, it must have mass, and it must be located at a height h above the earth’s surface.. It does not need to have any velocity.. Therefore, of the options above, the object must have mass.. It does not need to have any of the other listed options. 268 52. An star in space moves at 10 m/s, collides with and sticks to a second star.. The second star has the same mass as the first star and was initially at rest.. The kinetic energy of the combined mass is ___ that of the value of the first star.. a. 1x b. 2x c. 0.5X d. 4x e. Not enough information to be able to say Explanation:. The kinetic energy of a moving object is given by KE = 0.5*m*v*v, 269 where KE is the kinetic energy of the object, m is the mass of the object, and v is the velocity of the object.. The first star has a mass of M kg, and a velocity of 10 m/s (magnitude). The second star also has a mass of M kg, but an initial velocity of 0 m/s.. The combined initial momentum = M*10 = 10*M kg.m/s.. Due to conservation of momentum, the final combined momentum = the initial combined momentum.. Therefore the final combined momentum = 10M units.. The combined mass is 2M kg.. Therefore, the final speed is Final Combined Momentum/Combined Mass = 10M/2M = 5 m/s.. Now, the kinetic energy of the first star before the collision is 0.5*M*10*10 kg.m.m/s/s = 50M units.. And the kinetic energy of the combined star masses (after the collision) is 0.5*(2M)*5*5 kg.m.m/s/s = 25M units.. Therefore the KE of the combined mass is 0.5 times that of the first star before the collision (25M units vs.. 50M units). 53. Two railroad cars move towards each other at 10 m/s.. They collide and bounce backward at 20 m/s.. This event violates conservation of a. mass 270 b. acceleration c. KINETIC ENERGY d. potential energy e. collisions f. none of these g. all of these Explanation:. The total momentum of the cars before the collision is zero (since the two cars have the same mass, and move with the same speed, 10 m/s, in opposite directions, and the momentum P=m*v). The total momentum of the cars after the collision is zero (since the two cars have the same mass, and move with the same speed, 20 m/s, in opposite directions, and the momentum P=m*v). Therefore, momentum is conserved. How about kinetic energy (KE)? The KE before the collision is 0.5*M*10*10 (for the first car) + 0.5*M*10*10 (for the second car) = 200M units.. The KE after the collision is 0.5*M*20*20 (for the first car) + 271 0.5*M*20*20 (for the second car) = 400M units.. Therefore, the initial KE is NOT equal to the final KE. This means that this event violates conservation of kinetic energy. 272