inertia in motion Which is harder to stop

“inertia in motion”

Which is harder to stop?

momentum = mass x velocity

Both can have large momenta:

Example 6. 1 A 100 kg football player runs with a velocity of 4. 0 m/s straight down the field. A 1. 0 kg artillery shell leaves the barrel of a gun with muzzle velocity of 500 m/s. Which has the greater momentum (magnitude), the football player or the shell? pf = 400 kg m/s, ps = 500 kg m/s So the less massive shell has greater momentum!

How do you change momentum? If the momentum of an object changes, either the mass changes or the velocity changes. Most often it’s the velocity that changes, which means there is an acceleration, which means there must be a net external force! The greater the force, the greater the change in velocity, and then the greater the change in momentum!

But TIME is also important!

Newton’s Second Law F = ma = m (Δv/ Δt) F Δt = m Δv = Δ(mv) F Δt = Δp “Impulse” = change in momentum

Important point regarding ∆p The figure below shows a ball bouncing off a wall. What is the ball’s change in momentum during the bounce? What is the direction of the average force on the ball as it bounces?

Increasing momentum

Which would you pick?

Decrease momentum over a long time

Why does the egg not break when it hits the sheet?

Example 6. 4 A golfer drives a 0. 046 -kg ball from an elevated tee, giving the ball an initial horizontal speed of 40 m/s (about 90 mph). What is the magnitude of the average force exerted by the club on the ball during this time? 1800 N Follow-up: what if the golfer “follows through” with the same force for 1. 5 ms more time? How will velocity change?

Example 6. 5 A 70. 0 -kg worker jumps stiff-legged from a height of 1. 00 m onto a concrete floor. (a) What is the magnitude of the impulse he feels on landing, assuming a sudden stop in 8. 00 ms? (b)What is the average force? (a) 310 kg m/s (b) 38, 800 N (~8730 lbs)

Momentum over short time

Impulses are greater when bouncing takes place.

Conservation of momentum If you wish to accelerate an object, you must apply a force to it. (Newton’s second law) If you want to change the momentum of an object, you must exert an impulse on it. Basically the same thing!

Force or impulse must be exerted on the object by something outside the object. Internal forces do not count! Net momentum here is still zero!

Momentum is a vector quantity! + =0 If no net force acts on a system, then the momentum of that system cannot change.

No net external force!

Law of conservation of momentum In the absence of an external force, the momentum of a system remains unchanged.

Formulas Momentum: p = mv Impulse: F Δt = Δp