1. # 32 on next page!!!! 1 2 1 1 1 2 29. Step 1: Mass 1 goes down ramp
PE = KE
mgh = 1/2 m v2
9.8(.3) = 1/2 v2
v = 2.42 m/s
v1 - v2 = v21 - v11 =
2.42 =
v21 - v11
Step 2: Elastic collision between the two masses
Mass 1 collides with Mass 2 m2 = 0.5m1
m1v1 + m2v2 = m1v11 + m2v21
m1(2.42)+ 0= m1v m1v21
2.42 = v v21
Solve the two equations v11 = 0.81 m/s v21 = 3.23 m/s 1
Step 3: Motion in a Vertical Plane
y = 1/2 gt2
0.9 = 1/2 (9.8) t2
t = 0.43 seconds 2
x = v1t x = 0.81(0.43) x = 0.35m 35cm for Mass 1
x = 3.23(0.43) x = 1.39m for Mass 2
# 32 on next page!!!!
m1v12 =
KE1 = 1/2 m1v12
= .5 m1v12
KE2 = 1/2(1.5 m1)(.67v1)2
= .34 m1v12
KE1 + KE2 = 7500
.5 m1v12 +
.34 m1v12
= 7500
KE1 = .5 m1v12
KE2 = .34 m1v12
KE1 = .5 ( )
KE1 = J
4.46 kJ
KE2 = .34( )
KE2 = J
3.04 kJ
34. m2 = 1.5 m1
m1v1 + m2v2 = 0
m1v m1v2 = 0
v1 = - 1.5v2
v2 = - v1/1.5
v2 = - .67v1

2. ( ( ( ( θ If you can't memorize the formula can work it out
page Read example for formulas
these are used for a ballistic pendulum you must know how to do this! θ L h
Step 2 M m +
L - h x v1 M m
Step 1 L v
Conservation of Momentum
mv = (m+M)v1
Conservation of Energy
KE = PE
1/2 (m+M)(v1)2 = (m+M)gh
(v1)2 = 2(m+M)gh
(m+M)
(v1)2 = 2gh
v1 = √2gh
For Ballistic Pendulum
v = m+M (
√2gh (
v = m+M (v1) m
230 = m ( (
√2(9.8)h
.028
h = .16 m
If you can't memorize the formula can work it out
Conservation of Momentum
mv = (m+M)v1
.028(230) = ( ) v1
v1 = 1.78 m/s
Conservation of Energy
KE = PE
1/2 (m+M)(v1)2 = (m+M)gh
1/2 ( ) (1.782) = ( ) (9.8) h
h = .16 m
L - h
L = 2.8
L - h =
x2 = 2.82
x = .93 m 93 cm
L - h = 2.64 x

3. μ= 0.40 x1 v12 = x1 (-3v2)2 x1 (-3)2 35. v1 = 3.59v1 v1 = 23.79 m/s
m1v1 + m2v2 = (m1+ m2)v1
920v1+ 0= ( )v1
920v1 = 3300v1
Wf = KE (This is v1)
μmgx = 1/2 mv2
.8(9.8)(2.8) = 1/2 v2
v = 6.63 m/s
v1 = 3.59(6.63)
v1 ≈ 52mph
μ= 0.40
38.
m1v1 + m2v2 = 0
v1 = - 3 v2
Wf = KE
Mass 1 μm1gx1 = 1/2 m1v12
Mass 2 μ(3)m1gx2 = 1/2 (3)m1v22
x1 = v12
3x2 = 3v22
x2 = v22
x v12
x v22 =
x1 (-3v2)2
x1 (-3)2 x2 x1 9

4. 41.
m1v1x + m2v2x = (m1+ m2)vx
4.3(7.8) + 0= ( )vx
33.54 = 9.9 v cosθ
3.39 = v cosθ
x direction
y direction
m1v1y + m2v2y = (m1+ m2)vy
(10.2) = ( )vy
= 9.9 v sin θ
5.83 = v sin θ E1 E2 θ
v1x
E1+E2
v2y v
v sin θ
v cos θ
tan θ = θ =
v2 =
v = 6.74 m/s
v =
300
1.8 m/s
1.1 m/s
42.
1.1 cos 300
1.1 sin 300 a b
mavax + mbvbx = mavax1 + mbvbx1
x direction
mavay + mbvby = mavay1 + mbvby1
y direction
.4(1.8) + 0 = .4(1.1 cos 300) + .5 vbx1
0 = .4(1.1 sin 300) + .5 vby1
vbx1 = .68
vby1 = -.44 θ
.68
.44
= v2
v = .81 m/s
tan θ = .44/.68
θ =
v = 0.81 m/s below the + x axis
v = 0.81 m/s @