How Can the Work-Energy Theorem Be Applied to Calculate Block Speed?

[dsptl]

Speed Problem (Please Help!)

* A system of blocks is released from the rest. the speed of 10kg block just before it hits the ground the ground. The surface is frictionless.


http://img80.imageshack.us/img80/6199/24722704da3.jpg


Attempt:

I hv donw this way, but I am suppose to use work-kinetic energy theoreom or something to find the answer, which i hv no clue abt it...thought u guys would help me



first i found acceleration: a = g(M -m1sin45 - m2sin45)/(M+m1+m2) = 4.31 m2/s2

then used vf2 = vi2 +2ax = 0 + 2(4.31)(5) = 42.23m2/s2

and vf = 6.5m/s

but i need get this answer by Work-Kinetic theorem or something...Please HElp

Thanks in advacne

 

[Redbelly98]

Use conservation of energy. Write an expression for the total energy just before things start moving. Then write an expression for the total energy when the block hits the ground.

 

[dsptl]

Use conservation of energy. Write an expression for the total energy just before things start moving. Then write an expression for the total energy when the block hits the ground.

our professor slightly went over it...can u please just write the expression, I can work tht out

Thanks a lot for helping

 

[Redbelly98]

The exact equations should be in your textbook. There is (gravitational) potential energy and kinetic energy to account for.

 

[dsptl]

The exact equations should be in your textbook. There is (gravitational) potential energy and kinetic energy to account for.

but there r 3 blocks how do i add them together for the energy?

starting: (m1+m2+m3)gh = .5(m1+m2+m3)v*v

but I the height is not given for all the blocks...

 

[Redbelly98]

(m1+m2+m3)gh = .5(m1+m2+m3)v*v

There are two problems here.

1. The heights are all different. So you'll have to use h1, h2, and h3 for the heights of each block. Don't worry that the heights are not all given, it will work out in the end.

2. Potential and kinetic energies are not equal to each other. Instead, you add them together, to find the total energy of the 3 blocks.

 

[f(x)]

Or you can simply find the acceleration of the system using Newton's laws, and then calculate the final velocity using equations of motion