For the apparatus shown in the figure, there is no slipping between the cord and
ID: 2116791 • Letter: F
Question
For the apparatus shown in the figure, there is no slipping between the cord and the surface of the pulley. The blocks have mass of 3.0 kg and 5.7 kg, and the pulley has a radius of 0.12 m and a mass of 10.3 kg. At the instant the 5.7 kg mass has fallen 1.5 m starting from rest, find the speed of each block. (Assume the pulley is in the shape of a uniform solid disk and has no friction in its axle.) Figure:
And...
The position of an object that is oscillating on an ideal spring is given by the equation x=(12.3cm)cos[(1.26s%u22121)t].
(a) At time t=0.815 s, how fast is the object moving?
(b) At time t=0.815 s, what is the magnitude of the acceleration of the object?
Explanation / Answer
accn of system = (m1-m2)g/(m1+m2+I/r^2)standard result...
a= 2.7g/(8.7+5.15) = .2g ...
v= sqrt(2a*1.5) = sqrt(.6g) = 2.42 m/s
B)so v = - 12.3*1.26 sin 1.26t at t= .815 s v = -13.26 cm/s ...it going toward eqm position... x at t=.815 s is 6.36 cm ... so the accn = w^2 x = 1.26^2*6.36 cm/s^2 = 10.1 cm/s^2
just differentiate the eqns and put time values