1994M1. A 2-kilogram block and an 8-kilogram block are both attached to an ideal spring ( for which k=200N/m ) and both are initially at rest on a horizontal frictionless surface, as shown in the diagram above.
In an initial experiment, a 100-gram ( 0.1 kg ) ball of clay is thrown at the 2-kilogram block. The clay is moving horizontally with speed v when it hits and sticks to the block. The 8 -kilogram block is held still by a removable stop. As a result, the spring compresses a maximum distance of 0.4 meters.
a. Calculate the energy stored in the spring at maximum compression.
b. Calculate the speed of the clay ball and 2-kilogram block immediately after the clay sticks to the block but before the spring compresses significantly.
c. Calculate the initial speed v of the clay.
In a second experiment, an identical ball of clay is thrown at another identical 2-kilogram block, but this time the stop is removed so that the 8 -kilogram block is free to move.
d. State whether the maximum compression of the spring will be greater than, equal to, or less than 0.4 meter. Explain briefly.
e. State the principle or principles that can be used to calculate the velocity of the 8-kilogram block at the instant that the spring regains its original length. Write the appropriate equation(s) and show the numerical substitutions, but do not solve for the velocity.