Question

A massless pan hangs from a spring that is suspended from the ceiling. When empty, the pan is 50 cm below the ceiling. If a 100 g clay ball is placed gently on the pan, the pan hangs 60 cmbelow the ceiling. Suppose the clay ball is dropped from the ceiling onto an empty pan.

Part A

What is the pan's distance from the ceiling when the spring reaches its maximum length?

Express your answer to two significant figures and include the appropriate units.

L =

Answer 1

After the clay ball is gently put on the pan, the net force on the pan zero once it displaces by 10 cm. So

So, F_grav = F_spring

=> mg = k[L - L_o]

=> (0.100)(9.8) = k(0.60 - 0.50]

=> k = 9.8 N/m

Now when the clay ball is dropped from the ceiling, the ball acquires some kinetic energy. By Work Energy Theorem, the change in Potential Energy will bring about change in Kinetic Energy.

Therefore mg[h - h_o] = (1/2)m(v² - u²) = 0.100(9.8)(0.5) = 0.490 J

Once the ball reaches the pan, this energy will get stored in the pan in the form of elastic potential energy thereby displacing it.

So, 0.490 = (1/2)kx²

where x is the displacement from the mean position L_o = 0.5 m

=> 0.490 = (1/2)(9.8)x²

=> x = 0.3162 m = 31.62 cm.

therefore the pan's distance from the ceiling is L = 50 + 31.62 = 81.62 cm.