Question

A spring is used to launch a block up a frictionless ramp as shown at right. At time t\, the spring is compressed and the block is released from point A. The block moves up the ramp, losing contact with thespring at point B. When it passes point C, the block has a velocity v_c directed up the ramp.

Imagine a system that includes the block and possibly one or more additional objects.

a. Is it possible to choose a system whose total energy is constant during the interval from t₁ to t2? If so, state which object(s) must be included in the system. Explain.

b. Is it possible to choose a system so that the total energy is NOT constant during the interval from t_{ to ?₂? if so what is the system containing the fewest possible objects for which the energy is not constant during this interval. Explain.

Answer 1

a) The frictionless ramp , the block and the spring , must be included in the system so that total energy is constant during the interval from t₁ to t2 . As because if we consider these as a isolated system then all the work done by and against will be in the system itself. There will be no other energy losses outside this system. Fo example ... As the block moves up the ramp , the ramp will also start moving towards the right and will gain some kinetic energy too , which is at the loss of kinetic energy of the block , gain in gravitational potential energy of the block , and loss in spring potential energy. So if we consider whole of it as a system we can apply conservation of energy.

b) yes it is possible to choose a system so that the total energy is NOT constant during the interval from t_{ to t2 . If we consider only the block as our system then initially there was no energy , then it gains kinetic energy and potential energy. So energy does not remain constant and we cannot apply law of conservation of energy.