Please answer the final question at the bottom GOAL Use conservation of energy to calculate the speed of ablock on a horizontal spring with and without friction.PROBLEM A block with mass of 5.00 kg is attached to ahorizontal spring with spring constant k = 4.00 x 102 N/m, asin the figure. The surface the block rests upon is frictionless. Ifthe block is pulled out to x, = 0.0500 m and released, (a)X:find the speed of the block when it first reaches the equilibriumpoint, (b) find the speed when x = 0.0250 m, and (c)repeat part (a) if friction acts on the block, with coefficient H= 0.150.A mass attached to a spring.STRATEGY In parts (a) and (b) there are no nonconservative forces, so conservation of energy, can beapplied. In part (c) the definition of work and the work-energy theorem are needed to deal with the loss ofmechanical energy due to friction.SOLUTION(A) Find the speed of the block at the equilibrium point.Start with the conservation of energy(KE + PE, + PE,), = (KE + PE, + PE,);equation.(1) mv? + ? - mv? +Substitute expressions for the block'skinetic energy and the potentialenergy, and set the gravity terms tozero.= v?Substitute v, = 0, x, = 0, and multiplyby 2/m.Solve for v, and substitute the given4.00 x 102 N/m (0.0500 m)5.00 kgV =Vvalues.= 0.447 m/s(B) Find the speed of the block at the halfway point.Set v, = 0 in Equation (1) and multiplykx?= v? +kx?by 2/m.mSolve for v, and substitute the givenV = VK(x? - x7)mvalues.4.00 x 102 N/m r(o.050 m)? - (0.025 m)?]5.00 kg= 0.387 m/s(C) Repeat part (a), this time with friction.Apply the work-energy theorem. Thework done by the force of gravity andWnc = mv? - mv?the normal force is zero because theseforces are perpendicular to the motion.Substitute v, - 0, x, - 0, and%3DWtric -Hnx,.Set n = mg and solve for v,.mv? -kx? - mmgx,V = Vx - 2gx,m4.00 x 102 N/m (0.050 m)? - 2(0.150)(9.80 m/s?)(0.0505.00 kg0.230 m/s=LEARN MOREREMARKS Friction or drag from immersion in a fluid damps the motion of an object attached to aspring, eventually bringing the object to rest.QUESTION In the case of friction, what percent of the mechanical energy was lost by the time the massfirst reached the equilibrium point? (Hint: use the answers to parts (a) and (c).)%

Name: Please answer the final question at the bottom GOAL Use conservation o
Uploaded: 2024-03-20T06:57:25.000Z
Channel: Bartleby
Description: Please answer the final question at the bottom GOAL Use conservation of energy to calculate the speed of ablock on a horizontal spring with and without friction.PROBLEM A block with mass of 5.00 kg is attached to ahorizontal spring with spring consta