Momentum

Impulse and momentum

Albina | Rauan | Tamerlan

Discussion

1)Will you be able to safely pass by the tennis table?

2)What about the football field?

Terminology

momentum - дене импульсы/импульс тела

impulse - күш импульсы/импульс силы

Poll

Basketball and tennis ball move at the same speed. Which one does have more “quantity” of motion? Why?

• Basketball ball

• Tennis ball

Explanation

of Survey

Momentum

Momentum is the most important quantity when it comes to handling collisions in physics. Momentum is a physical quantity defined as the product of mass multiplied by velocity. 
 $p\ =\ m\ \cdot\ \upsilon$  

 $\upsilon$  - velocity [m/s]
m - mass [kg]

Impulse

When you apply a force for a certain amount of time, you create an impulse. In fact, that’s the definition of impulse — impulse equals the force applied multiplied by the time it was applied. Here’s the equation:

 $I=F\cdot t$   
F - force [N]
t - time [s]

Poll

Force of impulse

How long will it take to get the bodies to move at the same speed?

• More time for a

• More time for b

Answer

It is clear that case b takes more time. We can show it by combining 2 formulas:

Impulse - Momentum Theorem

The impulse due to all forces acting on an object (the net force) is equal to the change in momentum of the object

Example

A car having a mass of 900 kg is moving to the east at a velocity of 10 m/s. Calculate

a) the momentum of the car

b) the impulse when velocity increases to 30 m/s in 5 seconds

Solution

a and b

CONSERVATION OF MOMENTUM

You will define law of conservation

Terminology

interact - əсерлесу/взаимодействовать

collision - соқтығыс / соударение

elastic collision-серпімді соқтығысу/упругое столкновение

inelastic collision-серпімсіз соқтығысу/неупругое столкновение

Inelastic collision

is a collision in which there is a loss of kinetic energy. While momentum of the system is conserved in an inelastic collision, kinetic energy is not.

Elastic collision

is a collision in which there is no net loss in kinetic energy in the system as a result of the collision. Both momentum and kinetic energy are conserved quantities in elastic collisions.

Example

Two objects of masses m₁ = 6 kg and m₂ =2 kg approach each other with speeds v₁ =2 m/s and v₂ = 4 m/s and undergo a head-on elastic collision.  Find the velocities of the objects after the collision.

Solution

Since the collision is elastic, both energy and momentum are conserved.

Mass m₁ will move with a speed of 1 m/s in the negative direction, and mass m₂ will move with a speed of 5 m/s in the positive direction.

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Are you ready?

10 questions

Multiple Choice

Impulse formula?

• $p=m\cdot\upsilon$

• $I=F\cdot t$

• $m_1\upsilon_{1i}+m_2\upsilon_{2i}=m_1\upsilon_{1f}+m_2\upsilon_{2f}$

• $m_1\upsilon_{1i}+m_2\upsilon_{2i}=\left(m_1+m_2\right)\cdot\upsilon_c$

Multiple Choice

What kind of collision?

• elastic collision

• inelastic collision

• both

Multiple Choice

Momentum formula?

• $p=m\cdot\upsilon$

• $I=F\cdot t$

• $m_1\upsilon_{1i}+m_2\upsilon_{2i}=m_1\upsilon_{1f}+m_2\upsilon_{2f}$

• $m_1\upsilon_{1i}+m_2\upsilon_{2i}=\left(m_1+m_2\right)\cdot\upsilon_c$

Multiple Choice

What kind of collision?

• elastic collision

• inelastic collision

• both

Multiple Choice

Elastic collision formula?

• $p=m\cdot\upsilon$

• $I=F\cdot t$

• $m_1\upsilon_{1i}+m_2\upsilon_{2i}=m_1\upsilon_{1f}+m_2\upsilon_{2f}$

• $m_1\upsilon_{1i}+m_2\upsilon_{2i}=\left(m_1+m_2\right)\cdot\upsilon_c$

Multiple Choice

Inelastic collision formula?

• $p=m\cdot\upsilon$

• $I=F\cdot t$

• $m_1\upsilon_{1i}+m_2\upsilon_{2i}=m_1\upsilon_{1f}+m_2\upsilon_{2f}$

• $m_1\upsilon_{1i}+m_2\upsilon_{2i}=\left(m_1+m_2\right)\cdot\upsilon_c$

Multiple Choice

An average force of 40 N which is parallel to the ground is applied to a billiard ball in 0.02 s. What is the impulse applied to the ball?

• 0,8 N*s

• 0,4 N*s

• 0,2 N*s

• 0,1 N*s

Multiple Choice

A basketball player is bouncing on a flat surface. The time of interaction of the ball with the surface is $\frac{1}{600}\ s$   and the impulse that the surface applies to the ball is 3 Ns. 

• 200 N

• 400 N

• 1600 N

• 1800 N

Multiple Choice

Two 2 kg balls moving with velocities of 4 m/s and 2 m/s on a smooth horizontal surface undergo a head – on inelastic collision, as shown in the figure. What is the common velocity of the balls after the collision?

• 4 m/s

• 3 m/s

• 2 m/s

• 1 m/s

Multiple Choice

A 2 kg ball moving with a velocity of 20 m/s on a frictionless horizontal surface undergoes a head–on inelastic collision with another object, as shown in the figure. If they move off together after the collision, what is the common velocity of the balls?

• 20 m/s

• 10 m/s

• 8 m/s

• 4 m/s