A spring (70 N/M) has an equilibrium length of 1.00 m.The spring is compressed t

Question

A spring (70 N/M) has an equilibrium length of 1.00 m.The spring is compressed to a length of 0.50 m and a mass of1.8 kg is placed at its free end on a frictionless slope whichmakes an angle of 41 degrees with respect to the horizontal. Thespring is then released. Part A) If the mass is not attached to the spring,how far up the slope will the mass move before coming torest? Part B) If the mass is attached to the spring, howfar up the slope will the mass move before coming to rest? PartC) Now the incline has a coefficient of kineticfriction Uk. If the block, attached to the spring, is observed tostop just as it reaches the spring's equilibrium position, what isthe coefficient of friction Uk? A spring (70 N/M) has an equilibrium length of 1.00 m.The spring is compressed to a length of 0.50 m and a mass of1.8 kg is placed at its free end on a frictionless slope whichmakes an angle of 41 degrees with respect to the horizontal. Thespring is then released. Part A) If the mass is not attached to the spring,how far up the slope will the mass move before coming torest? Part B) If the mass is attached to the spring, howfar up the slope will the mass move before coming to rest? PartC) Now the incline has a coefficient of kineticfriction Uk. If the block, attached to the spring, is observed tostop just as it reaches the spring's equilibrium position, what isthe coefficient of friction Uk? If the mass is not attached to the spring,how far up the slope will the mass move before coming torest? Part B) If the mass is attached to the spring, howfar up the slope will the mass move before coming to rest? If the mass is attached to the spring, howfar up the slope will the mass move before coming to rest? PartC) Now the incline has a coefficient of kineticfriction Uk. If the block, attached to the spring, is observed tostop just as it reaches the spring's equilibrium position, what isthe coefficient of friction Uk? Now the incline has a coefficient of kineticfriction Uk. If the block, attached to the spring, is observed tostop just as it reaches the spring's equilibrium position, what isthe coefficient of friction Uk?

Explanation / Answer

k = 75 N/m
L = 1.00 x = 0.50m M = 1.9kg = 41 Part A potential energy of the spring = kinetic energy of the springat equilibrium position             ( 1/ 2) kx^ 2 = ( 1/ 2) M v^ 2 from this speed v = x [ k / M ]= 3.1414 m V = 0 (final velocity) acceleration a = - g sin = - 6.429 from the relation V ^ 2 - v^ 2= 2sS the distance along the ramp is S = [ V^2 -v^2 ] / 2a=0.7674 m (0.7674 m above the equilibrium position) Part B From law of conservation of energy , distance along the ramp = 0.5 m (0.5 m above the equilibrium position) Part A potential energy of the spring = kinetic energy of the springat equilibrium position             ( 1/ 2) kx^ 2 = ( 1/ 2) M v^ 2 from this speed v = x [ k / M ]= 3.1414 m V = 0 (final velocity) acceleration a = - g sin = - 6.429 from the relation V ^ 2 - v^ 2= 2sS the distance along the ramp is S = [ V^2 -v^2 ] / 2a=0.7674 m (0.7674 m above the equilibrium position) Part B From law of conservation of energy , distance along the ramp = 0.5 m (0.5 m above the equilibrium position)

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