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SWoo

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Thread moved from the technical forums, so no HH Template is shown.

A spring of spring constant k sits on a frictionless horizontal table, one end of the spring is attached to a wall the other end to a block of mass M= 2kg, also resting on the frictionless table. Another block of mass m=450g moving at a speed of 7m/s collides in-elastically with the block of mass M, as a result of the collision M moves in such a direction so as to compress the spring, which takes 0.4 seconds to reach maximum compression.

for a. what happens before removing M is that it oscillates alone and has separated from m. which is why now, you can remove M.

a. You now remove M when the system is at the point where v=0, How much time does it take for the mass M to go from having one third of its maximum kinetic energy to having 1/5 of its maximum kinetic energy as it is moving away form equilibrium.

doubling the mass doubles the energy so using the equation 1/2(2m)(v)^2=mv^2, you know that the Ek is changed by a factor of 2. however, apparently this is wrong. any ideas on how to solve it? to help solve the question, here are some hints:https://gyazo.com/2d8e1281d78037d5c8e0427075a23f00

b. The sphere of mass M and radius R shown rolls without slipping on the ground. It is attached at the top to a spring of spring constant k. The other end of the spring is attached to a wall. The system is in equilibrium, then you move the sphere by a small amount and the system goes into oscillation, find the period for small oscillations in terms of the quantities given.

I used this equation to solve the second part, but again, not getting the right answer. w0 = square root of mgR/I. Hints: https://gyazo.com/5d49cbb19ab59b85ec336f2205af7e23

c. A bar of length L is suspended from its top edge where it is free to rotate about the pivot, its bottom is connected to a horizontal spring of spring constant k the other end of the spring is connected to wall. Find the period of small oscillations for this bar.

used the same equation as b. hints: https://gyazo.com/d3b5f13dfed5554a037d0767977b8389

for a. what happens before removing M is that it oscillates alone and has separated from m. which is why now, you can remove M.

a. You now remove M when the system is at the point where v=0, How much time does it take for the mass M to go from having one third of its maximum kinetic energy to having 1/5 of its maximum kinetic energy as it is moving away form equilibrium.

doubling the mass doubles the energy so using the equation 1/2(2m)(v)^2=mv^2, you know that the Ek is changed by a factor of 2. however, apparently this is wrong. any ideas on how to solve it? to help solve the question, here are some hints:https://gyazo.com/2d8e1281d78037d5c8e0427075a23f00

b. The sphere of mass M and radius R shown rolls without slipping on the ground. It is attached at the top to a spring of spring constant k. The other end of the spring is attached to a wall. The system is in equilibrium, then you move the sphere by a small amount and the system goes into oscillation, find the period for small oscillations in terms of the quantities given.

I used this equation to solve the second part, but again, not getting the right answer. w0 = square root of mgR/I. Hints: https://gyazo.com/5d49cbb19ab59b85ec336f2205af7e23

c. A bar of length L is suspended from its top edge where it is free to rotate about the pivot, its bottom is connected to a horizontal spring of spring constant k the other end of the spring is connected to wall. Find the period of small oscillations for this bar.

used the same equation as b. hints: https://gyazo.com/d3b5f13dfed5554a037d0767977b8389