Mass m A = 5.47 kg sits on a frictionless, horizontal surface. A massless string
ID: 2191525 • Letter: M
Question
Mass mA = 5.47 kg sits on a frictionless, horizontal surface. A massless string is tied to mA, passes over a pulley (a solid disk of mass Mp = 6.78 kg and radius Rp = 49.5 cm), and is tied to mB = 3.77 kg hanging in space. Assume:
- the system starts from rest
- the string does not slip on the pulley
- the string is always perpendicular to the radius of the pulley
a) Find a, the magnitude of the acceleration of the masses.
1 m/s2
b) Find v, the speed of the masses after mB has fallen distance h = 3.94 m.
2 m/s
c) Find W, the work that has been done on the pulley after mB has fallen distance h = 3.94 m
3 J
d) Suppose the frictionless, horizontal surface can be tilted at any angle. At what angle ?, measured from the horizontal, would the surface have to be tilted so mass mB falls at a constant speed?
4o
Explanation / Answer
a)the acceleration of the blocks :
a = F/(m + kM) ----> m = mass of the translational object =mA+mB= 9.24 kg
----> M = mass of the rotational object = mass of pulley = 6.78 kg
F = force = weight of the hanging block = 3.77 * 9.8 = 36.95 N
k for a disk = 1/2
--> a = 36.95/(9.24 + (1/2)*6.78) = 2.93 m/s^2
b) v^2 = u^2 + 2 * a * d
= 0 + 2 * 2.93 * 3.94
v = 4.81 m/s
c)the angular velocity of the pulley at this time :
= v/r=9.71 rad/s
KE=.5I^2 ;I=.5mr^2
KE=39.22 J
d)