Momentum

Momentum

There are 4 really important things to know about momentum. The first is how momentum is defined, as the product of mass times velocity:

momentum : p = mv

 

The second note is built into this equation; momentum is a vector, and the momentum has the same direction as the velocity.

Impulse-Momentum Change Equation
         In a collision, a force acts upon an object for a given amount of time to change the object's velocity. The product of force and time is known as impulse. The product of mass and velocity change is known as momentum change. In a collision the impulse encountered by an object is equal to the momentum change it experiences.

Impulse = Momentum Change

F • t = mass • Delta v

         Again, this is a vector equation, so the change in momentum is in the same direction as the force.

CONSERVATION MOMENTUM

Types of collisions: (momentum is conserved in each case)

• elastic - kinetic energy is conserved
• inelastic - kinetic energy is not conserved
• completely inelastic - kinetic energy is not conserved, and the colliding objects stick together after the collision.

The total energy is always conserved, but the kinetic energy does not have to be; kinetic energy is often transformed to heat or sound during a collision.

Impulse Momentum Exam and  Problem Solutions

1. Objects shown in the figure collide and stick and move together. Find final velocity  objects.

Using conservation of momentum law;

m₁.V₁+m₂.V₂=(m₁+m₂).V_final

3.8+4.10=7.V_final

64=7.V_final

V_final=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.

a) Using conservation of momentum law;
(m₁+m₂).V=m₁.V₁+m₂.V₂

5.4=30+2.V₁

V₁=-5m/s

b) E_Kinitial=1/2/m₁+m₂).V²

E_Kinitial=1/2.5.16=40joule

E_Kfinal=1/2.2.5²+1/2.3.10²

E_Kfinal=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)

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.

 

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.

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).V_final

0,5.2=2.V_final

V_final=0,5m/s

 Thank :  http://www.physicstutorials.org/home/exams/impulse-momentum-exams-and-solutions/impulse-momentum-exam2-and-solutions