Question

A 1.4 kg block oscillates back-and-forth with a period of 4.5 s while it is attached to spring. When the block is instantaneously at rest at the spring’s maximum extension, a 1.1 kg blob of clay is dropped onto the block. How long does the block and clay take to complete one full back-and-forth oscillation now?

Answer 1

The new period of oscillation after adding a 1.1 kg blob of clay to the 1.4 kg block attached to a spring can be calculated by determining the spring constant from the initial period and applying it with the new combined mass.

Step-by-step explanation:

The oscillation period of a mass attached to a spring is given by the formula T = 2π√(m/k), where T is the period, m is the mass, and k is the spring constant. When a 1.1 kg blob of clay is added to the 1.4 kg block, the new total mass becomes 2.5 kg. Since the spring constant k remains unchanged, the new period T' can be found by using the initial period, T, and solving for k from the first scenario and then using it to find T' for the combined mass of the block and clay.

Initial period equation for 1.4 kg block:

T = 2π√(1.4 kg/k)

Period equation for combined mass:

T' = 2π√((1.4 kg + 1.1 kg)/k) = 2π√(2.5 kg/k)

By solving these equations, we can calculate the new period for the system with the added mass.