Impulse & Momentum

Recall…§Newton’s 1st law of motion: if no net force acts on a body, its

velocity is constant§Newton’s 2nd law of motion: velocity of a body is changed by

a net force acting on it

What is Momentum?

§Momentum (p): a measurement of “mass in motion” or “moving inertia”§Measures how hard it is to stop a moving object§Vector quantity§Units: kg⋅m/s (or N⋅s)

p = m × vm = mass , v = velocity

You Try!

Determine the momentum of a…§60 kg halfback moving eastward at 9 m/s

§540 kg⋅m/s, east§1000-kg car moving northward at 20 m/s

§20,000 kg⋅m/s, north§40-kg freshman moving southward at 2 m/s

§80 kg⋅m/s, south

How is Velocity Affected by Force?§Since all objects have mass, this means in order to have momentum,

they must have a velocity

The greater the mass, the greater the momentumThe greater the velocity, the greater the momentum

Which of these two objects has more momentum?

Do these two objects have the same momentum?

You Try!

A car possesses 20 000 units of momentum. What would be the car's new momentum if ...§ its velocity was doubled.

§40,000 kg⋅m/s (momentum is doubled)§ its velocity was tripled.

§60,000 kg⋅m/s (momentum is tripled)§both its velocity was doubled and its mass was doubled.

§80,000 kg⋅m/s (momentum is quadrupled)

Momentum & Force

§Newton’s 2nd law of motion can help explain how the momentum of an object is changed by a net force acting on it

F∆t = m∆vor

F∆t = ∆p

§Fnet = ma

§Fnet = mvf − vi

∆t

§Fnet = m vf − m vi

∆t

§Fnet = ∆p∆t

Momentum & Impulse

§ Impulse, J: force acting over time§Produces a change in momentum§Unit = Newton-second (N⋅s)

§Greater the impulse = greater will be the change in momentum§To have a change in momentum, there must be a force applied during

a time intervalJ = F∆tJ = ∆p

“Impulse” “Change in momentum”

F∆t = m∆v

Sample ProblemDetermine the impulse of a football halfback experienced a force of 800 N for 0.9 s to the north.Given:F = 800 Nt = 0.9sUnknown:J = ?

You Try!

Equation:J = F∆t

Substitute & Solve:J = 800 N (0.9 s)

= 720 N⋅s

§ A hockey player applies an average force of 80 N to a hockey puck for 0.2 s. Determine the impulse experienced by the hockey puck.§ 16 N⋅s

§ A 0.10-kg model rocket’s engine is designed to deliver an impulse of 6.0 N⋅s. If the rocket’s engine burns for 0.75 s, what is the average force the engine produces?§ 8.0 N

Impulse-Momentum Theorem

§ Impulse of an object is equal to the change in momentum that it causes

F∆t = ∆p or F∆t = p2 − p1

F∆t = m∆vJ = m∆vJ = ∆p

Sample Problem

A tow-truck applies a force of 2000 N on a 2000 kg car for a period of 3 s. What is the magnitude of the change in the car's momentum? Given:

F = 2000 Nm = 2000 kgt = 3 s

Unknown:∆p = ?

Equation:F∆t = ∆p

Substitute & Solve:∆p = F∆t

= (2000 N)(3 s)

= 6000 N·s

Sample Problem

An impulse of 11 N·s from a rocket engine has 0.0125 g of fuel. What is the exhaust velocity?Given:

J = 11 N·s m = 0.0125 kg

Unknown:v = ?

Equation:J = m∆v

Substitute & Solve:J = m∆v

11 N·s = (0.0125 kg) ∆v880 m/s = ∆v

v = 880 m/s

You Try!

While waiting in a car at a stoplight, an 80 kg man and his car are suddenly accelerated to a speed of 5 m/s as the result of a rear end collision. Assuming the time taken to be 0.3 s, find:

a. The momentum of the man b. The force exerted on him by the back of the seat of the car.

a. 400 kg⋅m/s b. 1333 N

A Bullet traveling at 500 m/s is brought to rest by an impulse of 50 N⋅s. What is the mass of the bullet?

m = 0.1 kg