Momentum, Impulse, and Collisions

Honors Physics

Momentum

Momentum ( റ𝑝) is the product of mass and velocity

Momentum is a vector. It has a direction, so + and – signs matter.

Used to analyze collisions

Units: 𝑘𝑔∙𝑚

𝑠

റ𝑝 = 𝑚 റ𝑣

ExampleAn 80 kg running back is running 6 m/s and a 90 kg linebacker is running 5 m/s.

Which has more momentum?

a) The running back

b) The linebacker

c) They are the same

Which has more inertia?

a) The running back

b) The linebacker

c) They are the same

ExampleAn 80 kg running back is running 6 m/s and a 90 kg linebacker is running 5 m/s.

Which has more momentum?

a) The running back

b) The linebacker

c) They are the same

Which has more inertia?

a) The running back

b) The linebacker

c) They are the same

Impulse

Defined as the change in

momentum (∆ റ𝑝)

Defined as the product of

force and time ( റ𝐹𝑡)

Units: either 𝑁 ∙ 𝑠 OR 𝑘𝑔∙𝑚

𝑠

∆ റ𝑝 = റ𝐹𝑡

ExampleIn the diagram, a 60-kilogram roller skater exerts a 10-newton force on a 30-kilogram roller skater for 0.20 second. What is the magnitude of the impulse applied to the 30-kilogram roller skater? What about Newton’s 3rd law?

a) 50 N∙s

b) 2.0 N∙s

c) 6.0 N∙s

d) 12 N∙s

ExampleIn the diagram, a 60-kilogram roller skater exerts a 10-newton force on a 30-kilogram roller skater for 0.20 second. What is the magnitude of the impulse applied to the 30-kilogram roller skater? What about Newton’s 3rd law?

a) 50 N∙s

b) 2.0 N∙s

c) 6.0 N∙s

d) 12 N∙s

Example

An 8.0 kg bowling ball is rolling along

with a momentum of 16 kgm/s East

and it hits a 1.5 kg bowling pin, slows

down, and continues rolling with

10 kgm/s East. What is the magnitude

of the impulse delivered to the ball?

a) 2 kgm/s

b) 6 kgm/s

c) 8 kgm/s

d) 26 kgm/s

Example

An 8.0 kg bowling ball is rolling along

with a momentum of 16 kgm/s East

and it hits a 1.5 kg bowling pin, slows

down, and continues rolling with

10 kgm/s East. What is the magnitude

of the impulse delivered to the ball?

a) 2 kgm/s

b) 6 kgm/s

c) 8 kgm/s

d) 26 kgm/s

Example

A bumper car is sliding along with a

momentum of 700 kgm/s East,

collides with the wall, and bounces

back going 200 kgm/s West. What

was the magnitude of the impulse

delivered to the bumper car?

a) 500 kgm/s East

b) 500 kgm/s West

c) 900 kgm/s East

d) 900 kgm/s West

Example

A bumper car is sliding along with a

momentum of 700 kgm/s East,

collides with the wall, and bounces

back going 200 kgm/s West. What

was the magnitude of the impulse

delivered to the bumper car?

a) 500 kgm/s East

b) 500 kgm/s West

c) 900 kgm/s East

d) 900 kgm/s West

Example

A 0.046 kg golf ball that is initially at rest,

is struck by a golf club. The impact lasts

0.00018 s and the ball left the club going

78 m/s East.

What is the impulse delivered to the ball?

What was the average force applied to

the ball?

∆ റ𝑝 = റ𝐹𝑡

Example

A 0.046 kg golf ball that is initially at rest,

is struck by a golf club. The impact lasts

0.00018 s and the ball left the club going

78 m/s East.

What is the impulse delivered to the ball?

What was the average force applied to

the ball?

∆ റ𝑝 = റ𝐹𝑡

Example

A person’s head of 5.0 kg is moving

25 m/s East when it collides with an

airbag and comes to a stop. The

collision with the airbag is 0.08 s.

What is the impulse delivered to the

person’s head?

What is the average force applied to

the person’s head?

∆ റ𝑝 = റ𝐹𝑡

Example

A person’s head of 5.0 kg is moving

25 m/s East when it collides with an

airbag and comes to a stop. The

collision with the airbag is 0.08 s.

What is the impulse delivered to the

person’s head?

What is the average force applied to

the person’s head?

∆ റ𝑝 = റ𝐹𝑡

Impulse and airbags

If an object comes to a stop, the

impulse is fixed, but it can stop over a

short time OR a long time.

An airbag will extend the time of the

collision so that the average force

delivered to person’s head decreases.

∆ റ𝑝 = റ𝐹𝑡

Impulse and “follow-through”

If a constant force is applied for a

longer time, the impulse delivered to

the object will increase.

∆ റ𝑝 = റ𝐹𝑡