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A 3 kg mass object is pushed 0.6 m into a spring with spring constant 210 N/m on a frictionless horizontal surface. Upon release, the object moves across the surface until it encounters a rough incline. The object moves UP the incline and stops a height of 1.5 m above the horizontal surface.
(a) How much work must be done to compress the spring initially?
(b) Compute the speed of the mass at the base of the incline.
(c) How much work was done by friction on the incline?

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Answer with Explanation:

We are given that

Mass of spring,m=3 kg

Distance moved by object,d=0.6 m

Spring constant,k=210N/m

Height,h=1.5 m

a.Work done  to compress the spring initially=[tex]\frac{1}{2}kx^2=\frac{1}{2}(210)(0.6)^2=37.8J[/tex]

b.

By conservation law of energy

Initial energy of spring=Kinetic energy  of object

[tex]37.8=\frac{1}{2}(3)v^2[/tex]

[tex]v^2=\frac{37.8\times 2}{3}[/tex]

[tex]v=\sqrt{\frac{37.8\times 2}{3}}[/tex]

v=5.02 m/s

c.Work done by friction on the incline,[tex]w_{friction}=P.E-spring \;energy[/tex]

[tex]W_{friction}=3\times 9.8\times 1.5-37.8=6.3 J[/tex]

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