Assume that there is energy for the masses to reach the spring and compress it b

Question

Assume that there is energy for the masses to reach the spring and compress it by any amount, how does the compression “z” depend on all of the other variables?

Homework 1 Due Thursday 2/25/16 A pendulum of length "L" with a mass "3m" is released from an angle "e". It swings to the bottom and hits a block of mass "m" elastically. The block slides on a rough surface over a distance of "x" with a coefficient of kinetic friction of "pk". The surface then becomes frictionless. The block continues and hits and sticks to another block of mass "2m". Both blocks then slide up a slope of angle "p" a distance "y" where they engage a spring of spring constant "k" compressing it by a distance "z" before stopping. Hk 3m 2m How many processes are there and what approach would you use to describe them? For next Tuesday, Assume that there is energy for the masses to reach the spring and compress it by any amount, how does the compression "z" depend on all of the other variables? page 1

Explanation / Answer

At very first the energy from the PE of the bob of the pendulum is converted into the KE at its bottom , which is then given to the mass ‘m’. Since ‘m’ slides on a rough surface some parts of this energy is used as a frictional force. When the mass ‘m’ ends rough surface it then collides with another bock ‘2m’ with the remained energy . Again here KE distribution takes place between ‘m’ and ‘2m’. Summation of KE of both block is the KE of ‘m’ before it hits the ‘2m’. Now both block climbs on the inclined plane , so their initial energy is used against the ‘gravity’ and the stop at the height ‘h’ where they finished their initial energy.

Thus at each step we have use either law of conservation of energy or law of conservation of momentum theorem or both.

The distance ‘z’ in this case can be calculated by using trigonometry,

sin= h/z

z= h/sin

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