Homework 8_133002400_ENGR_216_504
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Date
Apr 3, 2024
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ENGR 216 – Section 504
Pages
Homework 8: Collisions
1. After the collision what is the velocity of the ball?
Given:
Ball 1 mass = 5.00 kg
Ball 1 v
i
=
2.55
m/s
Ball 2 mass = 3.61 kg
Ball 2 v
i
=
1.55
m
/
s
Find:
a. What is the final velocity for ball 1?
b. What is the final velocity for ball 2? 0.1439
Diagram:
v
1
i
v
2
i
Theory: Use the conservation of momentum and the conservation of kinetic energy because the balls are
moving. The velocities are going to be solved for both x and y. The answer is going to be in a vector that contains both components of x and y.
F
ave
=
m∆ v
∆t
m
1
20
°
m
1
10
°
60
°
m
2
m
2
1
2
m
1
v
1
i
+
1
2
m
2
v
2
i
=
1
2
m
1
v
1
+
1
2
m
2
v
2
m
1
v
1
i
+
m
2
v
2
i
=
m
1
v
1
+
m
2
v
2
Assumptions: x
−
component
:
(
5
) (
2.55
)
cos
(
0
)
+
(
3.61
) (
1.55
)
cos
(
60
)
=
(
5
)
v
f
1
cos
(
20
)
+
(
3.61
)
(
v
f
2
)
cos
(
350
)
12.75
+
2.79775
=
4.6984631
v
f
1
+
3.555155988
v
f
2
12.75
+
2.79775
=
4.6984631
(
4.845845
+
0.6268699
v
f
2
1.71
)
+
3.555155988
v
f
2
15.54775
=
13.31385
+
1.72231
v
f
2
+
3.555
v
f
2
2.2338998
=
5.277466
v
f
2
v
f
2
=
0.423
15.54775
=
4.69846
v
f
1
+
1.504862583
14.042887
=
4.69846
v
f
1
v
f
1
=
2.98
=
2.99
=
3
y
−
component
:5
(
2.55
)
sin
(
0
)
+
3.61
(
1.55
)
sin
(
60
)
=
5
(
v
f
1
)
sin
(
20
)
+
3.61
v
f
2
sin
(
350
)
0
+
4.845845147
=
1.71
v
f
1
−
0.6268699
v
f
2
4.845845
+
0.6268699
v
f
2
=
1.71
v
f
1
4.845845
+
0.6268699
v
f
2
1.71
=
v
f
1
Solution:
v
f
1
=
2.98
m
/
s
v
f
2
=
0.423
m
/
s
2. The villain
Given:
The villain’s mass = 65.0 kg
The villain’s initial velocity = 9.26 m/s, speed = 0.150 m/s
The villain is knocked back at velocity = 8.52 m/s and angle of 20 degrees from horizontal.
Chuck Norris’ fist moves at velocity of 0.0745 m/s and 10 degrees from horizontal.
Find:
a. What is the mass of Chuck Norris’ fist?
b. How much kinetic energy is lost in the collision?
Diagram:
20
°
10
°
Theory:
Kinetic Energy lost
=
K
f
−
K
i
Assumptions:
m
1
(
0.15
)
cos
(
0
)
+
65
(
9.26
)
cos
(
180
)
=
m
1
(
0.0745
)
cos
(
350
)
+
(
65
) (
8.52
)
cos
(
20
)
m
1
(
0.15
)
cos
(
0
)
−
m
1
(
0.0745
)
cos
(
350
)
=
65
(
8.52
)
cos
(
20
)
−
65
(
9.26
)
cos
(
180
)
m
1
(
(
0.15
)
cos
(
0
)
−
(
0.0745
)
cos
(
350
)
)
=
1122.3
m
1
(
0.076
)
=
1122.3
m
1
=
14645.37496
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m
1
(
0.15
)
sin
(
0
)
+
65
(
9.26
)
sin
(
180
)
=
m
1
(
0.0745
)
sin
(
350
)
+
(
65
) (
8.52
)
sin
(
20
)
Kinetic Energy Initial Kinetic Energy = 2951.557
Final Kinetic Energy = 2399.8307
Solution: (a) chuck Norris fist is 14650 kg. (b) Loss in kinetic energy is 551.73 J.
3. What is Vin’s mass, in kg?
Given:
vin
'
sinitial velocity , v
1
=
9.660
Zane initial mass = 53.8 kg
Zane velocity, v
2
=
7.26
m
s
They hold on to each other.
The final velocity, v
3
=
5.164
m
s
Find: Find Vin’s mass, m
1
Diagram:
(
m
1
+
m
2
)
v
3
at
75
°
v
2
at
135
°
v
1
at
30
°
Theory: This collisionistotallyinelastic
:
m
1
v
1
i
+
m
2
v
2
i
=
(
m
1
+
m
2
)
v
3
Assumptions:
m
1
(
9.66
)
cos
(
30
)
+
53.8
(
7.26
)
cos
(
135
)
=(
m
¿¿
1
+
53.8
)(
5.164cos
(
75
)
)
¿
m
1
(
8.3658
)
−
276.187
=
m
1
(
1.3365
)
+
71.906
m
1
(
8.3658
−
1.3365
)
=
71.906
+
276.187
m
1
(
7.029
)
=
348.09
m
1
=
49.52
=
49.5
Solution: Vin’s mass = 49.52 or 49.5 kg.