A 3.48-kg mass is moving in an idealized frictionless tube.

Question

Initially, the tube runs straight for 1.18 meter horizontally at ground level before rapidly curving to turn vertically upwards, as shown in the figure. The vertical portion of the tube is completely filled by a relaxed spring with a spring constant of 1.63e+3 N/m. The mass reaches a maximum height of 0.234 meters. Assume that the mass immediately begins to compress the spring as it starts to move vertically. Calculate the initial velocity of the mass.

Answer 1

This can be solved by using conservation of energy.

The mass initially has kinetic energy, which is converted to the Potential Energy of the spring AND gravitational Potential Energy.

1/2 mv² = 1/2 kx² + mgh h and k are the same.

One equation, one unknown.

Solve for m.