Question
A block of mass m is suspened through a spring of spring constant k and is in equlibrium. A sharp blow gives the block an initial downward velocity v. How far below the equilibrium psitin, the block comes to an instantaneous rest?
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Solution: Klet us consider the blockthe spring+the earth as the system. The system has gravitatioN/Al potential energy corresponding to the force between the block and the earth as well as the elastic potential energy corresponding to the sring force. The total mechanicla energy includes kinetic enegy, gravitatioN/Al potential energy and elastic potential energy.
When the block is in equilibrium it is acted upon by two forces, a. the force of gravity mg and b. the tension in the spring . where x is the elongation. For equilibrium, mg=kx, so that the spring is stretched by a length 1/2 k(mg/k)^2=(m^2g^2)/(2k)1/2 mv^2+(m^2g^2)/(2k)1/2k9mg/k+h)^21/2mv^2+(m^2g^2)/(2k)=1/2k(mg/k+h)^2-mghh=vsqrt(m/k)\displaystyle
When the block is in equilibrium it is acted upon by two forces, a. the force of gravity mg and b. the tension in the spring . where x is the elongation. For equilibrium, mg=kx, so that the spring is stretched by a length 1/2 k(mg/k)^2=(m^2g^2)/(2k)1/2 mv^2+(m^2g^2)/(2k)1/2k9mg/k+h)^21/2mv^2+(m^2g^2)/(2k)=1/2k(mg/k+h)^2-mghh=vsqrt(m/k)\displaystyle
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Question Text | A block of mass m is suspened through a spring of spring constant k and is in equlibrium. A sharp blow gives the block an initial downward velocity v. How far below the equilibrium psitin, the block comes to an instantaneous rest? |
Answer Type | Text solution:1 |
Upvotes | 150 |