Can you solve question 8 and ONLY part c of question 10 ? A block of mass m = 1.

Question

Can you solve question 8 and ONLY part c of question 10 ?

A block of mass m = 1.5 kg is dropped from height h = 20 cm onto a spring of spring constant k = 1900 N/m. Find the maximum distance the spring is compressed. Did you conserve mechanical energy, from the release point to the (momentary) stopping point? In numbers or symbols, what are the initial and final values of kinetic energy, gravitational potential energy, and elastic potential energy? A block with mass m = 1.80 kg is placed against a spring on a frictionless incline with angle 6 = 30.0 Degree . (The block is not attached to the spring.) The spring, with spring constant k = 20.8 N/cm, is compressed 23.0 cm and then released. What is the elastic potential energy of the compressed spring? What is the change in the gravitational potential energy of the block-Earth system as the block moves from the release point to its highest point on the incline? How far along the incline is the highest point from the release point? Conserve mechanical energy from the moment of release to the moment when the block momentarily stops. What are the kinetic energy values at those two moments? What are the elastic potential energy values? What are the gravitational potential energy values? For the latter, you need to define a reference level for y = 0.

Explanation / Answer

8.

Using the law of conservation of energy,
Energy from block = Energy absorbed by spring
mg(0.20 + x) = (1/2)(k)x^2
where
m = mass of the block = 1.5 kg.
g = acceleration due to gravity = 9.8 m/sec^2 (constant)
x = compressed length of the spring
k = spring constant = 1900 N/m (given)

Substituting values,

1.5(9.8)(0.20 + x) = (1/2)(1900)(x^2)
14.7(0.20 + x) = 950x^2

Rewriting
950x^2 - 14.7x - 2.94 = 0

Using the quadratic formula,
x = 0.063 m

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