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for lunch you and your friends decide to stop at the nearest deli and have a sandwich made fresh for you with 0.300 kg of italian ham. the slices of ham are weighed on a plate of mass 0.400 kg placed atop a vertical spring of negligible mass and force constant of 200 n/m . the slices of ham are dropped on the plate all at the same time from a height of 0.250 m . they make a totally inelastic collision with the plate and set the scale into vertical simple harmonic motion (shm). you may assume that the collision time is extremely small. Express your answer numerically in meters and take free-fall acceleration to be g= 9.80m/s^2
What is the period of oscillation T of the scale?
Express your answer numerically in seconds.

Respuesta :

The period of oscillation T of the scale is T = 0.37 sec .

In the question ,

it is given that ,

weight of the Italian ham (m₁) = 0.300 Kg = 0.3 Kg

weight of the slices of ham are (m₂) = 0.400 kg = 0.4 Kg

the force constant of the vertical spring is(k) = 200 N/m .

Let oscillation period be = T ,

the plates make a totally inelastic collision ,

We know that , In inelastic collision, momentum is conserved but the kinetic energy is not conserved.

So , when the slice of ham land on the plate, then the kinetic energy of system equal to maximum potential energy of spring.

that means , T = 2π√(m₁ + m₂)/k

Substituting the values ,

we get ,

T = 2π√(0.3 + 0.4)/200

Simplifying further ,

we get ,

T = 0.37 seconds .

Therefore , If the collision is inelastic then the Period of oscillation is 0.37 s .

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