Question

Springs AB and CD have stiffness k1 and k2 respectively, both with an unstretched length of 600 mm. A 2-kg collar starts from rest when the springs are unstretched. Determine the speed of the collar when it has moved 200 mm.

a) Use v = sqrt(2k1/m)
b) Use v = sqrt(2k2/m)
c) Use v = sqrt((k1 + k2)/m)
d) Use v = sqrt(k1k2/m)

Answer 1

In a Physics problem that deals with the motion of a collar influenced by two springs, the appropriate formula to find the speed of the collar considers the combined energies stored in both springs. The correct formula is c) v = sqrt((k1 + k2)/m).

Step-by-step explanation:

The question pertains to the subject of Physics, more specifically it relates to the mechanics of springs and oscillations. Given the scenario where springs AB and CD have stiffnesses k1 and k2 respectively and a collar moves when the springs are unstretched, we are to determine the speed of the collar when it moves 200 mm.

The correct formula to determine the speed of the collar involves the conservation of energy principle, which states that the potential energy stored in the springs (when compressed or stretched) is converted into kinetic energy as the collar moves. In this case, we must consider the sum of the potential energies stored in both springs, since both springs influence the movement of the collar.

Therefore, the correct formula to use would be c) v = sqrt((k1 + k2)/m), where v is the speed, m is the mass of the collar, and k1 and k2 are the stiffness constants of springs AB and CD respectively.