Chapter 6:Momentum and Collisions

Coach KelsoePhysicsPages 196–227

Section 6–1:Momentum and Impulse

Coach KelsoePhysicsPages 198–204

Objectives

• Compare the momentum of different moving objects.

• Compare the momentum of the same object moving with different velocities.

• Identify examples of change in the momentum of an object.

• Describe changes in momentum in terms of force and time.

Linear Momentum

• Consider a soccer player heading a kick.

• So far the quantities and kinematic equations we’ve introduced predict the motion of an object, such as a soccer ball, before and after it is struck.

• What we will consider in this chapter is how the force and duration of the collision of an object affects the motion of the ball.

Linear Momentum

• The linear momentum of an object of mass m moving with a velocity v is defined as the product of the mass and velocity.

• Momentum is represented by the symbol “p,” which was given by German mathematician Gottfried Leibniz, who used the term “progress.”

• In formula terms: p = mv

Linear Momentum

• Momentum is a vector quantity, with its direction matching that of the velocity.

• The unit for momentum is kilogram-meters per second (kg·m/s), NOT a Newton, which are kilogram-meters per square seconds (kg·m/s2).

• The physics definition for momentum conveys a similar meaning to the everyday definition for momentum.

Sample Problem A

• A 2250 kg pickup truck has a velocity of 25 m/s to the east. What is the momentum of the truck?

Sample Problem Solution

• Identify givens and unknowns:–m = 2250 kg– v = 25 m/s east

• Choose the correct formula:– p = mv

• Plug values into formula:– p = (2250 kg)(25 m/s east)– p = 56,000 kg·m/s to the east

Changes in Momentum

• A change in momentum is closely related to force. You know this from experience – it takes more force to stop something with a lot of momentum than with little momentum.

• When Newton expressed his second law of motion, he didn’t say that F = ma, but instead, he expressed it as F = Δp/Δt.

• We can rearrange this formula to find the change in momentum by saying Δp = FΔt.

Impulse-Momentum Theorem

• The expression Δp = FΔt is called the impulse-momentum theorem.

• Another form of this equation that can be used is Δp = FΔt = mvf – mvi.

• The impulse component of the equation is the FΔt. This idea also helps us understand why proper technique is important in sports.

Sample Problem B

• A 1400 kg car moving westward with a velocity of 15 m/s collides with a utility pole and is brought to rest in 0.30 s. Find the force exerted on the car during the collision.

Sample Problem Solution

• Identify your givens and unknowns:–m = 1400 kg vi = 15 m/s west or -15 m/s

– Δt = 0.30 s vf = 0 m/s

– F = ?

• Choose the correct equation:– FΔt = mvf – mvi F = mvf – mvi/Δt

• Plug values into equation:– F = mvf – mvi/Δt

– F = (1400 kg)(0 m/s) – (1400 kg)(-15 m/s)/0.30 s– F = 70,000 N to the east

Impulse-Momentum Theorem

• Highway safety engineers use the impulse-momentum theorem to determine stopping distances and safe following distances for cars and trucks.

• For instance, if a truck was loaded down with twice its mass, it would have twice as much momentum and would take longer to stop.

Sample Problem C

• A 2240 kg car traveling to the west slows down uniformly from 20.0 m/s to 5.00 m/s. How long does it take the car to decelerate if the force on the car is 8410 N to the east? How far does the car travel during the deceleration?

Sample Problem Solution

• Identify givens and unknowns:– m = 2240 kg vi = 20.0 m/s west or -20.0 m/s

– vf = 5.00 m/s west or -5.00 m/s

– F = 8410 N east or +8410 N– Δt = ? Δx = ?

• Choose the correct formulas:– FΔt = Δp Δt = Δp/F

– Δt = mvf - mvi/F

• Plug values into formula:– Δt = (2240 kg)(-5.00 m/s) – (2240 kg)(-20.0 m/s)/8410 N– Δt = 4.00 s

Reducing Force

• We can reduce the force an object experiences by increasing the stop time.

• It’s the same idea behind catching a water balloon or an egg. The change is momentum is the same.

• The reason this works is that time and force are indirectly proportional. As one increases, the other decreases.

• It’s the difference between a bunt or a homerun!

Scrambled Eggs, Anyone?