Physics Help Forum Is this spring elastic problem erroneous?

 Energy and Work Energy and Work Physics Help Forum

 Aug 26th 2015, 01:10 PM #11 Junior Member   Join Date: Aug 2015 Posts: 3 If you guys don't mind, I had one more question that I'm probably overthinking as well. The answer to this question is D and I plugged in my own numbers to get that answer. However, I don't understand the concept. Why is it that dividing the velocity by two means you have to divide the Kinetic Energy by 4? I bolded "divide" because that's what "decrease by a factor" means to do. The kinetic energy E of an object is given by E = .5*m*v^2 where m is the object's mass and v is the velocity of the object. If the velocity of an object decreases by a factor of 2 what will happen its kinetic energy? A. Kinetic energy will increase by a factor of 2. B. Kinetic energy will increase by a factor of 4. C. Kinetic energy will decrease by a factor of 2. D. Kinetic energy will decrease by a factor of 4.
 Aug 26th 2015, 01:55 PM #12 Physics Team     Join Date: Jun 2010 Location: Naperville, IL USA Posts: 2,271 same principle as the earlier problem - the kinetic energy of an object is proportional to the velocity of the object squared. An object moving at 10 m/s has four times the KE of an object moving at half that speed. One way to see this is to calculate the ratio of the two energies: KE_1/K_2 = (0.5 m v_1^2)/(0.5 m v_2^2) = (v_1/v_2)^2 So if v_2 = one half v_1, then KE_2 = one quarter KE_1

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