# Question: An ideal spring of force constant k is hung vertically

An ideal spring of force constant k is hung vertically from the ceiling, and a held object of mass m is attached to the loose end. You carefully and slowly ease that mass down to its equilibrium position by keeping your hand under it until it reaches that position.

(a) Show that the spring’s change in length is given by d = mg/k.

(b) Show that the work done by the spring is Wsp = m2g2/2k.

(c) Show that the work done by gravity is Wg = m2g2/2k.

Explain why these two works do not add to zero. Since the overall change in kinetic energy is zero, you might think they should, no?

(d) Show that the work done by your hand is Whand = m2g2/2k and that the hand exerted an average force of half the object’s weight.

(a) Show that the spring’s change in length is given by d = mg/k.

(b) Show that the work done by the spring is Wsp = m2g2/2k.

(c) Show that the work done by gravity is Wg = m2g2/2k.

Explain why these two works do not add to zero. Since the overall change in kinetic energy is zero, you might think they should, no?

(d) Show that the work done by your hand is Whand = m2g2/2k and that the hand exerted an average force of half the object’s weight.

**View Solution:**## Answer to relevant Questions

A winch is capable of hauling a ton of bricks vertically two stories (6.25 m) in 19.5 s. If the winch’s motor is rated at 5.00 hp, determine its efficiency during raising the load. Since K = p2/2m, how can kinetic energy be lost in an inelastic collision while the total momentum is still con-served? Explain. A karate student tries not to follow through in order to break a board, as shown in Fig. 6.27. How can the abrupt stop of the hand (with no follow- through) generate so much force? Suppose the billiard ball in Fig. 6.31 approaches the rail at a speed of and an angle of 60o, as shown, but rebounds at a speed of 10 m/s and an angle of 50o. What is the change in momentum in this case? An automobile with a linear momentum of 3.0 x 104 kg ∙ m/s is brought to a stop in 5.0 s. What is the magnitude of the average braking force?Post your question