A horizontal spring attached to a wall has a force constant of k = 780 N/m. A bl

Question

A horizontal spring attached to a wall has a force constant of k = 780 N/m. A block of mass m = 1.60kg is attached to the spring and rests on a frictionless, horizontal surface as in the figure below.

A horizontal spring attached to a wall has a force constant of k = 780 N/m. A block of mass m = 1.60kg is attached to the spring and rests on a frictionless, horizontal surface as in the figure below. The block is pulled to a position xi = 6.60 cm from equilibrium and released. Find the potential energy stored in the spring when the block is 6.60 cm from equilibrium. 1.7 J Find the speed of the block as it passes through the equilibrium position. 1.457 m/s What is the speed of the block when it is at a position xi/2 = 3.30 cm?

Explanation / Answer

Potential energy stored = 0.5*k*x^2 = 0.5*780*(6.6/100)^2 = 1.7J

At equilibrium, entire potential energy = kinetic energy. Therefore: 0.5*m*v^2 = 1.7 => v = 1.457m/s

At, 3.30 cms, the total energy = kinetic energy + potential energy = 0.5mv^2 + 0.5kx^2. Now from conservation of energy, this is equal to 1.7J

So, 0.5*1.6*v^2 + 0.5*780*(3.3/100)^2 = 1.7 => v = 1.2625m/s

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