Answer: 85 J
Answer: 0.2 kJ
Answer: ­ 45 J
Answer: 0.85 m/s
Super Phil Bonus: Phil and his Scooter have a combined mass of 100 kg. The scooter starts with a velocity of 15 m/s. After passing over the various hills and frictional areas, and going through a wind tunnel 2 m long that exerts a constant force of 12 N, Phil and his scooter collide with a freakishly huge 1000 kg ball bearing hanging like a pendulum from a 5m long rope. If the scooter comes to a dead stop after the collision, what maximum angle will the pendulum swing out to? 2 m
12 N
m
4 m
θ = ?
4 m
μ=.3
μ=
.2
5 15 m/s
3 m
6 m
5 m
μ=
.4
= h
40o
70o
Ki ­ Wf ­ Ug + Wwind ­ Wf + Ug ­ Wf = Ugpendulum
1/2mv2 ­ μmgdcosθ ­ mgh + Fd ­ μmgd + mgh ­ μmgdcosθ = mgh
(1/2(100kg)(9.8m/s2)) ­ ((.2)(100kg)(9.8m/s2)(5m)(cos40o)) ­ ((100kg)(9.8m/s2)(4m)) + ((12N)(2m)) ­ ((.3)(100kg)(9.8m/s2)(3m) + ((100kg)(9.8m/s2)(6m)) ­ ((.4)(100kg)(9.8m/s2)(4m)(cos70o)) = ((1000kg)(9.8m/s2))h
(11250J) ­ (750.7J) ­ (3920J) + (24J) ­ (882J) + (5880J) ­ (536.3J) = (9800N)h
11065 J
= h
9800N
1.13 m = h
*But... h = L ­ Lcosθ
So... 1.13 m = (5m) ­ (5m)cosθ
And... θ = cos­1 ((5m) ­ (1.13m))
(5m)
= 39.3o