g = 9.8 m s 2 g = 9.8\frac{m}{s^2} g = 9.8 s 2 m
d = 300 m m d = 300mm d = 300 mm
r = d 2 = 150 m m = 0.15 m r = \frac{d}{2}= 150mm= 0.15m r = 2 d = 150 mm = 0.15 m
I f r = 3 N ∗ m I_{fr}= 3N*m I f r = 3 N ∗ m
I f r = F f r ∗ r I_{fr}= F_{fr}*r I f r = F f r ∗ r
F f r = I f r r = 3 0.15 = 20 N F_{fr}= \frac{I_{fr}}{r}=\frac{3}{0.15}=20N F f r = r I f r = 0.15 3 = 20 N
Let the load descend a distance h \text{Let the load descend a distance }h Let the load descend a distance h
E k = m v 2 2 E_k =\frac{mv^2}{2} E k = 2 m v 2
E p = − m g h E_p= -mgh E p = − m g h
E f r = F f r h E_{fr}=F_{fr}h E f r = F f r h
E k + E p + E f r = 0 E_k+E_p+E_{fr}=0 E k + E p + E f r = 0
m v 2 2 − m g h + F f r h = 0 \frac{mv^2}{2} - mgh +F_{fr}h=0 2 m v 2 − m g h + F f r h = 0
v 2 = 2 h ∗ ( m g − F f r ) m ( 1 ) v^2= \frac{2h*(mg-F_{fr})}{m}(1) v 2 = m 2 h ∗ ( m g − F f r ) ( 1 )
v = 2 h ∗ ( m g − F f r ) m v=\sqrt{ \frac{2h*(mg-F_{fr})}{m}} v = m 2 h ∗ ( m g − F f r )
v 2 = 2 a h v^2 = 2ah v 2 = 2 ah
From (1) \text{From (1)} From (1)
2 a h = 2 h ∗ ( m g − F f r ) m 2ah = \frac{2h*(mg-F_{fr})}{m} 2 ah = m 2 h ∗ ( m g − F f r )
a = ( m g − F f r ) m = 10 ∗ 9.8 − 20 10 = 7.8 m s 2 a = \frac{(mg-F_{fr})}{m}=\frac{10*9.8 -20}{10}=7.8\frac{m}{s^2} a = m ( m g − F f r ) = 10 10 ∗ 9.8 − 20 = 7.8 s 2 m
Answer: a = 7.8 m s 2 \text{Answer: }a =7.8\frac{m}{s^2} Answer: a = 7.8 s 2 m
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