Answer to Question #224937 in Mechanics | Relativity for Nea

Question #224937

a ball of mass 100g is thrown vertically from the edge of a table with a speed of 1.3 m/s to compress a spring of a coefficient of 120 n/m. what is the height of the table if the spring compressed to 10.6 cm


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Expert's answer
2021-08-11T09:54:00-0400

Mass of ball, m=100 g=100×103 kg=101 kgm=100\space g=100\times10^{-3}\space kg=10^{-1}\space kg

Speed of ball, v=1.3 m/sv=1.3\space m/s

Spring constant, k=120 N/mk=120\space N/m

Compression in spring, x=10.6 cm=0.106 mx=10.6\space cm=0.106\space m

Let height of the table =h= h

12mv2+mgh=12kx2\dfrac{1}{2}mv^2+mgh=\dfrac{1}{2}kx^2

h=(kx2mv2)2mg=0.601 mh=\dfrac{(kx^2-mv^2)}{2mg}=0.601\space m


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