Question

A 1.50 kg , horizontal, uniform tray is attached to a vertical ideal spring of force constant 180 N/m and a 260 g metal ball is in the tray. The spring is below the tray, so it can oscillate up-and-down. The tray is then pushed down 15.2 cm below its equilibrium point (call this point A) and released from rest.

How fast is the ball moving just as it leaves the tray? (Answer is NOT 1.67 m/s or 1.98 m/s)

Problem 14.71 Part A How high above point A will the tray be when the metal ball leaves the tray? (Hint: This does not occur when the ball and tray reach their maximum speeds.) A 1.50 kg , horizontal, uniform tray is attached to a vertical ideal spring of force constant 180 N/m and a 260 g metal ball is in the tray. The spring is below the tray, so it can oscillate up-and-down. The tray is then pushed down 15.2 cm below its equilibrium point (call this point A) and released from rest. h= 24.8 cm Submit My Answers Give Up Correct Part B How much time elapses between releasing the system at point A and the ball leaving the tray? t= 0.223 Submit My Answers Give Up Correct Part C How fast is the ball moving just as it leaves the tray? 1 1 .98 u = m/s Submit My Answers Give Up

Answer 1

Initial Energy stored in spring = 0.5*180*0.152 = 13.68 J
at h = 24.8 cm
PE gained = (1.5+0.26)*9.8*0.248 = 4.277 J
KE gained = 0.5(1.5+0.26)v^2 = 0.88v^2
By energy balance
0.88v^2 + 4.277 + 0.5*180*(0.248 - .152)^2 = 13.68
v = 3.121 m/s