Question

You attach one end of a spring with a force constant k = 693 N/m to a wall and the other end to a mass m = 1.62 kg and set the mass-spring system into oscillation on a horizontal frictionless surface as shown in the figure. To put the system into oscillation, you pull the block to a position xi = 6.76 cm from equilibrium and release it. A horizontal spring labeled k is attached on its left end to the base of a wall, and on its right end to a block labeled m that rests upon the floor. There are three points along the floor that are labeled. The first point is near the middle of the apparatus, and is marked x=0. To the right of that point is a point marked x=x_i/4. Directly under the block is a point marked x=x_i.

(a) Determine the potential energy stored in the spring before the block is released. _______ J

(b) Determine the speed of the block as it passes through the equilibrium position. _________ m/s

(c) Determine the speed of the block when it is at a position xi/4. __________ m/s

Answer 1

potential energy stored in the spring = 0.5 * k * x^2

potential energy stored in the spring = 0.5 * 693 * 0.0676^2

potential energy stored in the spring = 1.583 J

by conservation of energy

initial energy = final energy

1.583 = 0.5 * mv^2

1.583 = 0.5 * 1.62 * v^2

v = 1.3979 m/s

speed of the block = 1.3979 m/s

again by conservation of nergy

1.583 = 0.5 * k * (xi/4)^2 + 0.5 * mv^2

1.583 = 0.5 * 693 * (0.0676 / 4)^2 + 0.5 * 1.62 * v^2

v = 1.353 m/s

speed of the block when its position is xi/4 = 1.353 m/s