Question

A 2-kilogram block is attached to an ideal spring (for which k = 200N/m) and initially at rest on a horizontal friction less surface, as shown in the diagram.

 

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 spring is attached to a wall as shown. 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.

Answer 1

(a) U_sp = ½ k ∆x² = ½(200)(0.4)² = 16J

(b) Apply energy conservation K_{before compression} = U_{sp-after compression} 

½ (m_a + m_b) v² = U_sp 

½ (0.1 + 2)v² = 16

v = 3.9m/s

(c) Apply momentum conservation perfect inelastic 

p_before = p_after 

m_av_ai= (m_a + m_b) v_f

(0.1)v_ai = (0.1 + 2) (3.9)v_ai = 81.9m/s