11. Block A of mass 2.0kg and block B of mass 8.0 kg are connected as shown abov

Question

11. Block A of mass 2.0kg and block B of mass 8.0 kg are connected as shown above by a spring of spring constant 80 N/m and negligible mass. The system is being pulled to the right across a horizontal frictionless surface by a horizontal force of 4.0N, as shown, with both blocks experiencing equal constant acceleration.

http://img389.imageshack.us/img389/8096/loldrawingbx5.png

a) Calculate the force that the spring exerts on the 2.0kg block.
b) Calculate the extension of the spring.

The system is now pulled to the left, with the 4.0N force pulling the smaller block first, and the spring connecting this to the larger block. Both blocks again experience equal constant acceleration.

c) Is the magnitude of the acceleration greater than, less than, or the same as before?
d) Is the amount the spring has stretched greater than, less than, or the same as before?
e) In a new situation, the blocks and the spring are moving together at a constant speed of 0.5 m/s to the left. Block A then hits and sticks to a wall. Calculate the maximum compression of the spring.

Explanation / Answer

so the acceleration on both blocks will have to be equal so
4=(8+2)a
a=.4m/s2

Force on the 2kg block will be:

F=2(.4)

F=.8 N

The spring is providing this force so

.8=.5(80)x2

x=.1414 m

Once again the acceleartion can be found the same way

4=(8+2)a
a=.4m/s2

The magnitude will be the same

Now the spring has to apply enough force to make a max 4 times are large accelerate the same speed, so the spring will be stretched more (4x to be exact)

Now we just set the kinetic energy equal to the potentital energy of a spring

.5(8).5^2=.5(80)x^2

x=.1581 m

Hope that helps

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