Solutions to Real Test 3

1.
(a) mgh = mv2  + HEAT.
 HEAT = 84.8 J

2.
(a) left
(b) right
(c) m1g h = m1v1i2 so that v1i = 9.9 m/s ...
Use 
(A) m1v1i = m1v1f + m2v2f  and use 
v1i - v2i = 9.9 - 0 = v2f - v1f   or
(B) 9.9 = v2f - v1f  
Solve (A)   and (B) for v1f = -3.3 m/s and v2f= 6.6 m/s
Use  m2g h2 = m2v2f2 so that h2 = 2.2 m
(d) m1g h1 = m1v1f2 so that h1 = 0.56 m
3.(a)
M2gH = (M1 + M2)V2 + IV2/R2 .... Be careful that both masses are moving!!
V= 3.13 m/s
(b) V2 = 2aH    so that a = 2.45 m/s2
4.
MgH = MV2 + Iv2/R2   so that v = 5.11 m/s = answer to part (b)
(a) w = v/R = 5.11 m/s