A spring with a spring constant k = 30 N/m is on a frictionless incline with an angle of 40º.  A 4.0 kg object is hung on the spring and allowed to slide down the incline.  What is the speed of the object after it has slid a distance D = 0.7 m?  Hint:  Make potential energy zero at the stretch of D

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Chapter1: Units, Trigonometry. And Vectors
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A spring with a spring constant k = 30 N/m is on a frictionless incline with an angle of 40º.  A 4.0 kg object is hung on the spring and allowed to slide down the incline.  What is the speed of the object after it has slid a distance D = 0.7 m?  Hint:  Make potential energy zero at the stretch of D.

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According to the law of conservation of energy , energy can neither be created nor destroyed but can only be converted from one form to another . Thus the initial potential energy of the object will be converted to the spring potential energy and kinetic energy of the object as it reaches distance D=0.7 m , thus mgh=12kD2+12mv2 , where m=4 kg is the mass of the object , g=9.8 m/s2 is the acceleration due to gravity , h is the height , k=30  N/m is the spring constant  and is the final velocity .

 

The height of the object is calculated by using the trigonometric formula ,

sinθ=hDh=Dsinθ=0.7 m×sin40°0.45 m

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