Homework8
Chapt. 11 & 12
Delivering Rescue Supplies
You are a member of an alpine rescue team and must project a box of supplies, with mass
, up
an incline of constant slope angle
so that it reaches a stranded skier who is a vertical distance
above the bottom of the incline. The incline is slippery, but there is some friction present, with
kinetic friction coefficient
.
Ei(total)f
k
Δ
S = Ef(total)
Ki = 0 , Ui = mgh, f
k
=
μ
k
N = =
μ
k
mg cos
α
,
Δ
S = h/sin
α
Kf = ½ mV
f
2
, Uf = 0
Therefor
½ mV
f
2
= mgh 
μ
k
mg cos
α
·h/sin
α
→
Vf =
2
2
cos
/ sin
k
gh
gh
μ
α
α
+
12.22.
Model:
The disk is a rotating rigid body.
Visualize:
The radius of the disk is 10 cm and the disk rotates on an axle through its center.
Solve:
The net torque on the axle is
A A
A
B B
B
C C
C
D D
D
sin
sin
sin
sin
(30 N)(0.10 m)sin(
90
)
(20 N)(0.050 m)sin90
(30 N)(0.050 m)sin135
(20 N)(0.10 m)sin0
3 N m
1 N m
1.0607 N m
0.94 N m
F r
F r
F r
F r
τ
φ
φ
φ
φ
=
+
+
+
=

° +
° +
° +
°
= 
+
+
= 
Assess:
A negative torque means a clockwise rotation of the disk.
12.27.
Model:
Two balls connected by a rigid, massless rod are a rigid body rotating about an axis through the center
of mass. Assume that the size of the balls is small compared to 1 m.
Visualize:
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We placed the origin of the coordinate system on the 1.0 kg ball.
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 Spring '10
 ZHOU
 kg

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