Question

A block weighing 10 N is attached to the lower end of a vertical spring (k = 200 N/m), the other end of which is attached to a ceiling. The block oscillates vertically and has a kinetic energy of 2.0 J as it passes through the point at which the spring is unstretched. Maximum kinetic energy of the block as it oscillates is :

• A. (a) 2.0 J
• A. (b) 2.25 J
• A. (c) 2.5 J
• A. (d) 2.64 J

Answer 1

(b)

Maximum KE is acquired by the block when it passes the mean position of SHM where ΣF = 0 or mg = k x.

x = mg/k = - $\frac{10}{200} = \frac{1}{20}$ m

Applying work energy theorem from position A to B on the block

K_f - K_i = W_gravity + W_spring

⇒ K_f - 2J=10N $\left( \frac{1}{20}m \right) + \left\lbrack - \frac{1}{2} \times 200 \times \left( \frac{1}{20} \right)^{2} \right\rbrack$

⇒ k_f = 2.25J.