kg sit shows a spring mounted vertically with a platform on top. Initially a blo

Question

kg sit shows a spring mounted vertically with a platform on top. Initially a block of mass m 25 s on the spring. It is held down, compressing it 1.1 m from its equilibrium position. Assume the spring is massless and does not extend beyond its equilibrium position. The spring constant is 20,000 N/m. After the spring is released, ow fast is the block moving when it is 3.0 m above the equilibrium position of the spring? A potential energy vs position graph is shown for a 1 kg particle moving along the x axis. if the particle has a total energy of 4.0 J, do the following: a) indicate points or regions where on the graph it slows down. b) indicate points or regions on the graph where it speeds up. c) indicate where the kinetic energy of the particle is a maximum. d) What is the speed of the particle at x = 2m? e) What is the force on the particle at x = 0.5 m?

Explanation / Answer

here,

mass , m = 25 kg

spring constant , K = 20000 N/m

x = 1.1 m

h = 3 m

let the speed of block be v

using conservation of energy

0.5 * k * x^2 = m * g * ( h + x) + 0.5 * m * v^2

0.5 * 20000 * 1.1^2 = 25 * 9.81 * ( 3 + 1.1) + 0.5 * 25 * v^2

solving for v

v = 29.8 m/s

the speed of block at h = 3 m is 29.8 m/s

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