Academic Integrity: tutoring, explanations, and feedback — we don’t complete graded work or submit on a student’s behalf.

1. A block of mass m is falling from the height h on to the plate of the spring

ID: 2123896 • Letter: 1

Question

1.      A block of mass m is falling from the height h on to the plate of the spring weight balance (plate%u2019s mass M, spring constant k) as shown. The block sticks to the balance and the system starts to oscillate in the vertical direction. Find the amplitude A of the oscillations.

A block of mass m is falling from the height h on to the plate of the spring weight balance (plate%u2019s mass M, spring constant k) as shown. The block sticks to the balance and the system starts to oscillate in the vertical direction. Find the amplitude A of the oscillations.

Explanation / Answer

Conserve energy: Pre collision velocity of mass m is: mgh = 0.5 m v^2 => v = sqrt(2gh)

Conserve initial and post collision momentum i.e.: mv = (M+m) v ' => v ' = mv/(M+m)

Amplitude of oscillation would be such that: 0.5 (M+m)v'^2 = 0.5 k A^2

=> A = [(M+m)/k]^(0.5) x v' = [(M+m)/k]^(0.5) * m/(M+m) * sqrt(2gh) = m * sqrt(2gh) / sqrt(k * (M+m))