Impulse Momentum Exam2 and Problem Solutions

Impulse Momentum Exam2 and  Problem Solutions
 
 
1. Objects shown in the figure collide and stick and move together. Find final velocity  objects.
 
collision_1
 
 
 
 
 
 
Using conservation of momentum law;
m1.V1+m2.V2=(m1+m2).Vfinal
3.8+4.10=7.Vfinal
64=7.Vfinal
Vfinal=9,14m/s
 
2. 2kg and 3kg objects slide together, and then they break apart. If the final velocity of m2 is 10 m/s,
a) Find the velocity of object  m1.
b) Find the total change in the kinetic energies of the objects.
 
collision_2
 
 
 
 
 
 
 
a) Using conservation of momentum law;
(m1+m2).V=m1.V1+m2.V2
5.4=30+2.V1
V1=-5m/s
 
b) EKinitial=1/2/m1+m2).V2
EKinitial=1/2.5.16=40joule
EKfinal=1/2.2.52+1/2.3.102
EKfinal=175 joule
Change in the kinetic energy is =175-40=135 joule
 
 
 
3. As shown in the figure below, object m1 collides stationary object m2. Find the magnitudes of velocities of the objects after collision. (elastic collision)
collision_3
 
 
 
 

 
 
In elastic collisions we find velocities of objects after collision with following formulas;
V1'=(m1-m2)/(m1+m2).V1
 
V2'=(2m1/m1+m2).V1
 
m1=6kg, m2=4kg, V1=10m/s
V1'=(6-4/6+4).10=2m/s
V2'=(2.6/6+4).10=12m/s
 
4. Momentum vs. time graph of object is given below. Find forces applied on object for each interval.
 
momentum_1
 
 
 
 
 
 
 
 
 
 
 
 
F.Δt=ΔP
F=ΔP/Δt
Slope of the graph gives us applied force.
I. Interval:
F1=P2-P1/10-0=-50/10=-5N
II. Interval:
F2=50-50/10=0
III. Interval:
F3=100-50/10=5N

5. A box having mass 0,5kg is placed in front of a 20 cm compressed spring. When the spring released, box having mass m1, collide box having mass m2 and they move together. Find the velocity of boxes.
 
 
 
momentum_2
 
 
 
 
 
 
 
 
Energy stored in the spring is transferred to the object m1.
1/2.k.X2=1/2.mV2
50N/m.(0,2)2=0,5.V2
V=2m/s
Two object do inelastic collision.
m1.V1=(m1+m2).Vfinal
0,5.2=2.Vfinal
Vfinal=0,5m/s
 
  
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