Introduction to Momentum

Strandbeest, Theo Jansen

Objectives

1. Define momentum and identify its key variables.
2. Explain the relationship between momentum, force, and time.
3. Apply the momentum equation to solve basic problems.

Prediction

What happens to a rolling ball if it hits a stationary object?

What factors affect how the rolling ball will behave?

What factors affect how the stationary object will behave?

Momentum is the key concept that governs these interactions.

Momentum (linear)

p = mv

m is mass in kg

v is velocity in m/s

p is momentum in kg·m/s

Some key points about momentum

• Momentum is a vector quantity...it has direction because velocity has direction
• Momentum is directly related to mass
• Momentum is directly related to velocity

What examples of momentum can you think of?

• Can a small car and a large truck ever have the same momentum?
• How would volleyball change if instead of a volleyball you used a bowling ball?

Momentum Can Be Transferred

Demo: Basketball vs. Tennis Ball

As you saw in the demo, momentum can be transferred according to the Law of Conservation of Momentum. (More on this later in the week.)

Try on Your Own

Experiment 1

• Get in groups of 3 or so and go to a station that has a track and cart.
• Give the cart a gentle push and see how it responds.
• Add mass to the cart and give the cart the same gentle push and see how it responds.
• How did changing the mass affect the cart’s momentum?

Try on Your Own

Experiment 2

• Use the spring on the cart loaded half-way to launch the cart. How did this applied force affect the momentum of the cart?
• Now load the spring completely and launch the cart. How did this affect the momentum of the cart differently?
• How are force and momentum related?
• (More on this later.)

A little practice

A Ford F350 has a mass of 3400 kg (7500 lbs). A Smart Car has a mass of 680 kg (1500 lbs). What speed would a Smart Car have to travel in order to have the same momentum as a Ford F350 traveling at 29 m/s (65 mph)?

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Model (very gently) the following scenarios:

• Moving heavy cart crashes into stationary light cart.
• Moving light cart crashes into stationary heavy cart.
• Moving heavy cart crashes into moving light cart.
• Can the moving light cart crash into the moving heavy cart and both stop? What has to be true?

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A little more practice

A 5 kg object moving at 2 m/s collides with a stationary 3 kg object. What is the total momentum of the system before the collision?

p = mv = (5 kg)(2 m/s) = 10 kg m/s

What must the momentum of the system be after the collision according to the Law of Conservation of Momentum?

p_i = p_f = 10 kg m/s

Extension: If the two carts stick together after the collision, what is the speed of the two carts after the collision?

10 kg m/s = (5 kg + 3 kg)v

v = 1.25 m/s