TrainsTrains

MomentumMomentum

Which hurts more if it hits you?Which hurts more if it hits you? Why?Why?

Left one has more massLeft one has more mass Left one has more velocityLeft one has more velocity Left one has more momentum!Left one has more momentum!

MomentumMomentum What does the word What does the word momentummomentum mean to you? mean to you? Newton referred to what modern physicists term Newton referred to what modern physicists term

linear momentumlinear momentum as “ as “the quantity of motion…the quantity of motion…arising from velocity and the quantity of matter arising from velocity and the quantity of matter conjointly.”conjointly.”

In other words, the momentum of the body is In other words, the momentum of the body is proportional to both its mass and its velocity. proportional to both its mass and its velocity. By definition,By definition,

pp = m = mvv

It is a vector quantity that has units of a kg•m/s.It is a vector quantity that has units of a kg•m/s.

(There’s no short version, like with Force and (There’s no short version, like with Force and Energy)Energy)

Newton’s Second LawNewton’s Second Law If an object has a change in velocity, a net force must If an object has a change in velocity, a net force must

be acting on it.be acting on it. Similarly, since momentum is directly related to Similarly, since momentum is directly related to

velocity (as well as mass), a change in momentum also velocity (as well as mass), a change in momentum also requires a net force.requires a net force.

In fact, Newton originally expressed his second law of In fact, Newton originally expressed his second law of motion in terms of momentum rather than motion in terms of momentum rather than acceleration.acceleration.

( )o o o

net

m v v mv mv p p pF ma

t t t t

Change in MomentumChange in Momentum

Newton’s second Newton’s second law states that law states that the the net external force net external force acting on an object acting on an object is equal to the time is equal to the time rate of change of rate of change of the object’s the object’s momentum.momentum.

net

pF

t

Hammering a Nail…Hammering a Nail…

ImpulseImpulse When two objects—such as a hammer and a nail, a When two objects—such as a hammer and a nail, a

golf club and a golf ball, or even two cars—collide, golf club and a golf ball, or even two cars—collide, they can exert large forces on one another for a short they can exert large forces on one another for a short period of time.period of time.

The force is not constant in this case. However, The force is not constant in this case. However, Newton’s second law in momentum form is still useful Newton’s second law in momentum form is still useful for analyzing such situations by using average values.for analyzing such situations by using average values.

Written in this form, the law states that the net Written in this form, the law states that the net average force is equal to the time rate of change of average force is equal to the time rate of change of momentum: momentum: FF = = ΔΔpp//ΔΔt.t.

Rewriting the equation to express the change in Rewriting the equation to express the change in momentum, we have momentum, we have

FFΔΔt = t = ΔΔpp = = pp - - ppoo

ImpulseImpulse

The term FThe term FΔΔt is known as the t is known as the impulseimpulse of the force: of the force:

Impulse = Impulse = FFΔΔt = t = ΔΔpp = m = mvv – m – mvvoo

The SI unit of impulse is a N•s.The SI unit of impulse is a N•s.

Thus, Thus, the impulse exerted on a body is equal to the the impulse exerted on a body is equal to the change in the body’s momentum.change in the body’s momentum.

Why are you always instructed to “follow through” in Why are you always instructed to “follow through” in sports?sports?

BaseballBaseball

Who exerts the Who exerts the greater impulse on a greater impulse on a baseball…the baseball…the pitcher or the pitcher or the catcher?catcher?

Who exerts the Who exerts the greater force on a greater force on a baseball…the baseball…the pitcher or the pitcher or the catcher?catcher?

Pitchers and CatchersPitchers and Catchers

Catcher:

High force, short time

Ergo: Big mitt.

Pitcher:

Low force,

long time

Air BagsAir Bags

Air BagsAir Bags In an accident, the In an accident, the

magnitude of the magnitude of the acceleration is about 32 acceleration is about 32 g’s. Such an acceleration g’s. Such an acceleration means a net force about means a net force about 32 times the weight of the 32 times the weight of the dummy, clearly enough to dummy, clearly enough to cause serious injuries.cause serious injuries.

What does an air bag do?What does an air bag do? Increases the stopping Increases the stopping

distance (increase stopping distance (increase stopping time).time).

Allows the force to be Allows the force to be distributed over a much distributed over a much larger area (more on this larger area (more on this later).later).

Air Bags can be Air Bags can be dangerous too!dangerous too!

Problem #1Problem #1

A woman, driving a golf ball off a tee, gives A woman, driving a golf ball off a tee, gives the ball a velocity of 28 m/s. The mass of the ball a velocity of 28 m/s. The mass of the ball is 0.045 kg, and the duration of the the ball is 0.045 kg, and the duration of the impact with the golf club is 6 ms. (a) What impact with the golf club is 6 ms. (a) What is the change in momentum of the ball? is the change in momentum of the ball? (b) Determine the average force applied to (b) Determine the average force applied to the ball by the club?the ball by the club? Answer:Answer:

1.3 kg•m/s1.3 kg•m/s 220 N220 N

Problem #2Problem #2 A baseball (m=0.14 kg) has an initial A baseball (m=0.14 kg) has an initial

velocity of vvelocity of voo = 38 m/s as it approaches = 38 m/s as it approaches the bat. The applies a force that is much the bat. The applies a force that is much larger than the weight of the ball, and larger than the weight of the ball, and the ball departs from the bat with a final the ball departs from the bat with a final velocity of vvelocity of vf f = 58 m/s. The contact time = 58 m/s. The contact time between the bat and ball is between the bat and ball is ΔΔt = 4.0 x 10t = 4.0 x 10--

33 s. Find the average force exerted on s. Find the average force exerted on the ball by the bat.the ball by the bat. Answer:Answer:

3400 N3400 N