Suppose a spring with spring constant 6 N / m is horizontal and has one end atta

Question

Suppose a spring with spring constant 6 N / m is horizontal and has one end attached to a wall and the other end attached to a mass. You want to use the spring to weigh items. You put the spring into motion and find the frequency to be 0 .3 H z (cycles per second). What is the mass? Assume there is no friction. Mass = help (units) Hint: The frequency mentioned in the problem gives the number of occurrences or cycles of a repeating event per unit time. The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency.

Explanation / Answer

Moving the mass gives it potential energy, releasing that mass changes that potential to kinetic and then back again. The total energy of the mass is the sum of the kinetic and potential energies and is constant. E=K+U A) The max. potential energy is U=(1/2)kA^2 at the point when v=0 (K=0). E=(1/2)kA^2 At x=0, the mass has no potential energy only kinetic. (1/2)mv^2=(1/2)kA^2 v^2=kA^2/m v=A*sqrt(k/m) . . B.) At that point F=-kx=-k(0)=0. . . C.) Yes, there is no force to dissipate the energy. . . D.) At x=A/2, the potential energy is U=(1/2)k(A/2)^2=kA^2/8 K=(1/2)mv^2 K+U=(1/2)kA^2 (1/2)mv^2+kA^2/8=kA^2/2 mv^2=kA^2(4/8-1/8) v^2=kA^2/m*(3/8) v=A*sqrt(3k/8m) . . E.) Watch the units. Convert to meters. Use the solution from D. A=0.05 m v=0.05*sqrt(3(30)/8(0.75))=0.05*3.87 v=0.19 m/s

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