1. 1) BEFORE AFTER 2) BEFORE AFTER
PEi + KEi + Wc = PEf + KEf + Wn
1) BEFORE
AFTER
KEf = 0
Wc = PEf
PEf = mgh
Wc = mgh
Substitute:
Wc = 100(9.8)(1.5)
KEi = 0
1.5 m
PEi = 0
Wc = ?
Wc = 1470 J
PEi + KEi + Wc = PEf + KEf + Wn
Wn = 0
2) BEFORE
AFTER
3 (sin 30) = h
PEi = KEf
h = 1.5 m
mgh = ½mv2
KEi = 0 h
Substitute:
(2)(9.8)(1.5) = ½(2)(v2)
PEi = mgh
3.0 m
Wc = 0
KEf = ½mv2
PEf = 0
Wn = 0
v = 5.4 m/s

2. 3) BEFORE AFTER f =μFN FN = Fg = 9.8m f =(0.4)(9.8m) = 3.92m
PEi + KEi + Wc = PEf + KEf + Wn
3) BEFORE
AFTER
KEi = Wn
½mv2 = fΔd
KEf = 0
KEi = ½mv2
PEf = 0
PEi = 0
Substitute:
½(m)(8)2 = (3.92m)(Δd)
Wc = 0
Wn = fΔd
Δd = 8.16 m
f =μFN
FN = Fg = 9.8m
f =(0.4)(9.8m) = 3.92m

3. 4) BEFORE AFTER Need to use trig to find h adj cos(30) = 1.25
PEi + KEi + Wc = PEf + KEf + Wn
4) BEFORE
AFTER
Wc = PEf
KEi = 0
Wc = mgh
PEi = 0
KEf = 0
PEf = mgh
Substitute:
Wc = (3.0)(9.8)(0.15)
Wc = ?
Wc = 4.41 J
Wn = 0
Now use ‘after’ diagram as ‘before’ and make an ‘after’ diagram – then solve for velocity at the bottom
Need to use trig to find h
adj
1.25 m
cos(30) =
1.25
30°
1.25 m
adj = 1.1 m
v = 1.7 m/s h
thus h = 1.25 – 1.1 = 0.15 m

4. (2.6 m above the initial position)
PEi + KEi + Wc = PEf + KEf + Wn
5) BEFORE
AFTER
PEi = PEf + KEf
KEi = 0
KEf = ½mv2
PEi = ½kx2
½kx2 = mgh + ½mv2
PEf = mgh
Substitute:
½800(0.04)2 = (0.025)(9.8)(0.15) + ½(0.025)v2
Wc = 0
V = 6.9 m/s
Wn = 0
Now use ‘after’ diagram as ‘before’ and make an ‘after’ diagram – then solve for maximum height
h = 2.45 m above the muzzle
(2.6 m above the initial position)

5. 6) BEFORE AFTER Need to use trig to find h f =μFN
PEi + KEi + Wc = PEf + KEf + Wn
6) BEFORE
AFTER
PEi = KEf + Wn
mgh = ½mv2 + fΔd
KEi = 0 h
PEi = mgh
3.0 m
Wc = 0
KEf = ½mv2
Need to use trig to find h
PEf = 0
Wn = fΔd
3 (sin 30) = h
h = 1.5 m
Substitute:
(2)(9.8)(1.5) = ½(2)(v2) + (3.4)(3.0)
f =μFN
FN = Fg cos θ = (2)(9.8)(cos 30) = 17 N
v = 4.4 m/s
f =(0.2)(17) = 3.4 N

6. 7) BEFORE AFTER μ = 0.37 KEf = ½m1v2 PEf = 0 KEf = ½m2v2 KEi = 0
PEi = m2gh
Substitute:
(3)(9.8)(.8) = ½ (5)(1.5)2 + ½(3)(1.5)2 + (f)(.8)
PEi = 0
Wc = 0
Wn = fΔd
f = N
Equation:
PEi + KEi + Wc = PEf + KEf + Wn
f =μFN
PEi = KEf + KEf + Wn
FN = Fg = (5)(9.8) = 49N
m2gh = ½m1v2 + ½m2v2 + fΔd
18.15 = μ(49)
μ = 0.37