Problem/Solution: http://img832.imageshack.us/img832/1313/88791065.jpg
What happened to the work done by friction BEFORE colliding with the spring?
What happened to the work done by friction BEFORE colliding with the spring?
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The work done against friction before or after collision is converted to heat energy. Speed is not constant before making contact with the spring. You are given speed at the moment of impact and are asked to find the compression. The -ve root corresponds to the case where the mass is attached to spring and the spring is stretched by 0.25m. Then the mass speeds up as the spring reaches its unstretched length, PE of spring used up working against friction and giving KE to mass. The speed of the mass as spring reaches its unstretched length is then 1.2 m/s
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The initial velocity of the block is 1.2m/s
At the instance of collision, the velocity of the block is 1.2m/s as well
Since the change in the speed of the block between the initial point and the final point (before compressing the spring) is zero, there is no work done by friction prior to contacting the spring.
At the instance of collision, the velocity of the block is 1.2m/s as well
Since the change in the speed of the block between the initial point and the final point (before compressing the spring) is zero, there is no work done by friction prior to contacting the spring.
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The diagram is a little misleading, but the text definitely says that the speed at contact is Va=1.2 m/s. So I think you have to assume either that the "initial speed" started at the moment of contact with the spring (in spite of the diagram), or that the section of the surface to the left of the spring is frictionless. I agree this could have been written better.