Experiment 1

TITLE : IMPULSE AND MOMENTUM

1. Objective.

The objective of the experiments are to demonstration the impact of momentum by a variable Force of the football offensive player apply a force for a given amount of  time to crash the diffensive player to passes it.

2. Theory.

The principle of linear impulse and momentum is obtained by integrating the equation of motion with respect to time.  The equation of motion can be written

                       

åF = m a = m (dv/dt)

Separating variables and integrating between the limits v = v₁ at  t = t₁ and v = v₂ at t = t₂ results in

                                               

This equation represents the principle of linear impulse and momentum.  It relates the particle’s final velocity (v₂) and initial velocity (v₁) and the forces acting on the particle as a function of time.

Linear momentum:  The vector mv is called the linear momentum, denoted as L.  This vector has the same direction as v.  The linear momentum vector has units of (kg·m)/s

Linear impulse:  The integral òF dt is the linear impulse, denoted I.  It is a vector quantity measuring the effect of a force during its time interval of action. I acts in the same direction as F and has units of N·s

Application.

Football in Collide

When player B crash to player A it will generate a lot of momentum force to player A.

It can use a conservation of linear momentum to find velovity of V_A2 :

Conservation of linear momentum

+ ®   å m_i(v_i)₀  =  å m_i(v_i)₁

Before Impact

m_A(v_A1) + m_B(-v_B1) = m_A(-v_A2)+ m_B(-v_B2)………………..(1)

After Impact

Impulse and momentum on Player A (x-dir):

∫ F dt = m_A (v_A2) - m_A (v_A1) ……………….(2)

3. Appratus.

·         Two person.

·         Speed measurement (velocity).

·         Weight gauge.

4. Procedure.

·         Take two football player A and B and wrote every weight of them.

·         Separate them with some distance.

·         Mark point for two football player A and B to collied.

·         Ask football player A and B to collied togather run with full speed.

·         When player A and B running wrote speed (velocity) of them.

·         Then after player A and B collied togather, make observation wheater player A or player B move backward.

·         Then make some calculation. 

5. Expected result.

·         Mass of player Aand B (kg) =               70kg or 80kg                              

·         Velocity (m/s) =               1.5m/s or 3m/s                        

Conservation of linear momentum (x-dir):

m_A(v_A1) + m_B(v_B1) = m_A(v_A2)+ m_B(v_B2)

70 (1.5) + 80 (-3) = 70(V_A2) + 80(2)

(-135) = (70) v_A2 + 160

v_A2 = (-135) - (160) / 70

v_A2 = 0.012m/s

 Impulse and momentum on player A (x-dir):

m_A (v_A1)+ ∫ F dt = m_A (v_A2)

70 (1.5) - ∫ F dt = 70 (0.012)

∫ F dt = 105.84 N·s

So when the the player B with 80kg mass, 3m/s velocity and player A 80kg mass, 1.5m/s velocity in a collied togather it will have some force momentum, and the momentum being find by find the final velocity of the player A. then the impulse and momentum of player A are 105.84 N.s.

6. Conclusion.

6.1. Expected result.

In this issue the observation of this experiment can be find by momentum of the player B must more then player A to passes the from player A. By increasing a initial velocity of player B also can make a different and increase the momentum of player B to collide player A.

6.2. Related to industries.

In this experiment it can be related to industry of automotive. For example, it use for crash test to find a durability and safety the driver.