A 0.45-kg crow lands on a slender branch and bobs up anddown with a period of 1.5 s. An eagle flies up to the same branch,scaring the crow away, and lands. The eagle now bobs up anddown with a period of 4.8 s. Treating the branch as an ideal spring,find (a) the effective force constant of the branch and (b) the massof the eagle

The system is released from rest with no slack in the cable and with the spring stretched 200 mm. Determine the distance s traveled by the 3.6-kg cart before it comes to rest (a) if m approaches zero and (b) if m = 2.4 kg. Assume no mechanical interference and no friction. The distance s is positive if up the incline, negative if down. k = 105 N/m 3.6 kg 25° m Answers: (a) m = 0, S = (b) m = 2.4 kg, S = i

A 50 g mass on the end of a horizontal spring( k=80 N/m) is moving at a speed of 2m/s when 3.4cm from equilibrium. What is the maximum acceleration experienced by the mass?

A 1.005 m chain consists of small spherical beads, eachwith a mass of 1.00 g and a diameter of 5.00 mm, threaded on an elasticstrand with negligible mass such that adjacent beads are separated bya center-to-center distance of 10.0 mm. There are beads at each end ofthe chain. The strand has a spring constant of 28.8 N/m. The chain isstretched horizontally on a frictionless tabletop to a length of 1.50 m,and the beads at both ends are fixed in place. (a) What is the linear massdensity of the chain? (b) What is the tension in the chain? (c) With whatspeed would a pulse travel down the chain? (d) The chain is set vibratingand exhibits a standing-wave pattern with four antinodes. What isthe frequency of this motion? (e) If the beads are numbered sequentiallyfrom 1 to 101, what are the numbers of the five beads that remain motionless?(f) The 13th bead has a maximum speed of 7.54 m/s. Whatis the amplitude of that bead’s motion? (g) If x0 = 0 corresponds to thecenter of the 1st bead and x101 =…

(b) Neglecting all resistive forces, determine the spring constant. N/m (c) Neglecting all resistive forces, find the speed of the projectile as it moves through the equilibrium position of the spring (where x = 0), as shown in Figure (b). m/s

A bullet with mass 4.95 g is fired horizontally into a 1.972-kg block attached to a horizontal spring. The spring has a constant 5.71 x 102 N/m and reaches a maximum compression of 6.44 cm. (a) Find the initial speed of the bullet-block system. m/s (b) Find the speed of the bullet. m/s

A 1.60-kg object is held 1.15 m above a relaxed, massless vertical spring with a force constant of 310 N/m. The object is dropped onto the spring. (a) How far does the object compress the spring? (b) Repeat part (a), but this time assume a constant air-resistance force of 0.650 N acts on the object during its motion. m (c) How far does the object compress the spring if the same experiment is performed on the Moon, where g = 1.63 m/s2 and air resistance is neglected?