Act9_sol - 9.1 Activity 9 Solutions: Mass and Energy...

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12/12/05 1 Activity 9 Solutions: Mass and Energy 9.1 Einstein’s Equation Applied to Physical and Chemical Changes Your instructor will discuss Einstein’s equation, E = Mc 2 , which is probably the most important equation of the 20 th century. 1) Mass and Energy What is the relationship between mass and energy? Mass (or matter) can be converted into energy, and energy can be converted into mass as illustrated by Einstein’s equation E =Mc 2 . The constant c is the speed of light, 3 x 10 8 meters/second. The mass of an object can be increased by giving the object energy, and the mass of an object can be decreased by taking energy away from that object. 2) Einstein’s Equation applied to physical changes: stored potential energy Should adding energy to a spring by winding it change the mass of the spring? a) What is the mass of the free play radio in kilograms? __ about 1.70 kg __ b) Your instructor will turn the crank to wind the radio’s spring. Does the mass of the radio appear to change after the spring is wound? No c) How much force is needed to turn the radio’s handle at a constant speed? _ 13 N_ d) Find the distance in meters that the end of the handle travels in when it is turned one revolution by measuring the radius of the extended crank handle. The handle radius = 0.1 meter. The distance the end of the handle travels is the circumference of the circle = 2 π (0.1 m) = 0.63 meters e) Calculate the amount of work done to turn the handle one revolution. W = F D = 13 N x 0.63 m = 8.17 J f) The work done to turn the radio handle equals the energy added to the radio’s spring. Use your result from part f) and Einstein’s equation to find the additional mass of the radio as a result of winding its spring. use M = E/c 2 where E is the work you found in part e) M = 8.17 J/(9 x 10 16 m 2 /s 2 ) = 9.1 x 10 –17 kg g) How would the following physical changes affect the energy and mass of a substance? Energy Change Mass Change 1) A book is raised to a shelf. gravitational energy added increase 2) A spring is stretched. strain energy added increase 3) A car accelerates kinetic energy added increase 4) Liquid nitrogen boils. thermal energy added increase 5) Water is frozen into ice. thermal energy removed decrease h) Group Discussion Question: Would these changes in mass register on a scale? Why or why not?
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12/12/05 2 3) Einstein’s Equation applied to chemical changes a) What is the mass of a light stick in kilograms? _ approx 0.22 kg __ b) Break the light stick’s vial. What type of energy is given off? __ visible light___ Do you detect any infrared radiation? _No_ c) Examine a night light. What type of energy is given off? __ visible light___ Do you detect any infrared radiation? _No_ d) Since the light stick and the night light give off similar radiation, we compare the brightness of the light stick to the brightness of two night lights. If the light stick’s brightness is 10 times greater than the two night lights, what is the wattage of the light stick? (Hint: the wattage of the night lights is given on their back cover.) _ 1.0 watts _ e)
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Act9_sol - 9.1 Activity 9 Solutions: Mass and Energy...

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