Finding the max length of a spring

[DStan27]

Spring Force

A massless pan hangs from a spring that is suspended from the ceiling. When empty, the pan is 49 cm below the ceiling. If a 75 g clay ball is placed gently on the pan, the pan hangs 60 cm below the ceiling. Suppose the clay ball is dropped from the ceiling onto an empty pan. What is the pan's distance from the ceiling when the spring reaches its maximum length?
first i did k = .735/.11 = 66.8181
then i used k = mgh/d to find the max length
which was 66.8181 = 3.6015/d and got d = 5.39 but that wasn't the correct answer. can somebody help me with what i am doing wrong?

 

[siddharth]

A massless pan hangs from a spring that is suspended from the ceiling. When empty, the pan is 49 cm below the ceiling. If a 75 g clay ball is placed gently on the pan, the pan hangs 60 cm below the ceiling. Suppose the clay ball is dropped from the ceiling onto an empty pan. What is the pan's distance from the ceiling when the spring reaches its maximum length?
first i did k = .735/.11 = 66.8181
then i used k = mgh/d to find the max length
which was 66.8181 = 3.6015/d and got d = 5.39 but that wasn't the correct answer. can somebody help me with what i am doing wrong?

Why k = mgh/d?

 

[andrevdh]

h = 0.49 + d

 

[dx]

From the first part of the question, you can determine the spring constant. When the clay ball is just about to hit the pan, what is its kinetic energy? When the spring reaches maximum length, what is the kinetic energy of the clay ball? Zero. So, all the kinetic energy has been converted to spring potential energy. Since you already know the spring constant, can you tell how much it has to extend from its equilibrium position to have a potential energy equal to the kinetic energy of the ball?