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Momentum and Collisions

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Momentum

and Collisions

Physics 2053

Lecture Notes

Momentum and Collisions

Momentum and Collisions

Topics

6-01 Momentum and Impulse

6-02 Conservation of Momentum

6-03 Collisions

Momentum and Collisions

Momentum and Impulse

F

m

m

Momentum and Impulse

A block moving with an initial velocity vi is acted on by

a constant force F for a time Dt.

Momentum is a vector

Momentum and Collisions

Momentum and Impulse

Momentum and Impulse

Newton’s 2nd Law

p

Momentum and Collisions

Momentum and CollisionsProblem

v

A 12 kg hammer strikes a nail at a velocity of 8.5 m/s and comes to rest in a time interval of 8.0 ms.

(a) What is the impulse given to the nail?

m

(b) What is the average force acting on the nail?

Momentum and Collisions

Momentum and Collisions 07-01

The area under the curve on a Force versus time (F vs. t)

graph represents

A) impulse.

B) momentum.

C) work.

D) kinetic energy.

Momentum and Collisions

Conservation of Momentum

u1

v1

Fm

v = u

FM

M

M

M

m

m

m

u2

v2

Conservation

of

Momentum

p(before) = p(after)

Collision between to moving objects

Fm = - FM

FmDt = - FMDt

Dpm = -DpM

m(u2- u1) = -M(v2- v1)

mu2- m u1 = - Mv2+ Mv1

Mv1 + m u1 = Mv2+ mu2

Momentum and Collisions

Conservation of Momentum

V = ?

M

M

m

before

after

Collision with a stationary block

v

m

Momentum and Collisions

Momentum and Collisions07-08

A 9,300 kg boxcar traveling at 15.0 m/s strikes a second boxcar at rest. The two stick together and move off with a speed of 6.0 m/s. What is the mass of the second car?

.

Momentum and Collisions

Conservation of Momentum

V

after

before

Bullet fired into a block which is initially at rest.

v

M

m

mv

(M + m)V

Momentum and Collisions

Momentum and Collisions 07-01

A freight car moves along a frictionless level railroad

track at constant speed. The car is open on top.

A large load of coal is suddenly dumped into the car.

What happens to the velocity of the car?

A) It increases.

B) It remains the same.

C) It decreases.

D) cannot be determined from the information given

Momentum and Collisions

Collisions

Elastic Collisions

Momentum and Kinetic Energy

are both conserved

Inelastic Collisions

Only Momentum is conserved

Momentum and Collisions

Collisions

m1

m1

vf

m2

before

after

An Inelastic Collision

v1

v2

m2

Momentum and Collisions

Momentum and Collisions 07-01

In an inelastic collision, if the momentum is conserved,

then which of the following statements is true about

kinetic energy?

A) Kinetic energy is also conserved.

B) Kinetic energy is gained.

C) Kinetic energy is lost.

D) none of the above

Momentum and Collisions

Momentum and Collisions 07-01

Two objects collide and stick together.

Kinetic energy

A) is definitely conserved.

B) is definitely not conserved.

C) is conserved only if the collision is elastic.

D) is conserved only if the environment is frictionless.

Momentum and Collisions

Collisions

vA1

vB1

mA

mB

mA

mB

vA2

vB2

Elastic Collision (General Equations)

Momentum and Collisions

Collisions

mA

mB

vA2

vB2

Elastic Collision (vB1 = 0) Ball B is initially at rest.

vA1

mB

mA

Momentum and Collisions

Collisions

vA1

m

m

m

m

VB2

Elastic Collision (vB1 = 0 and mA= mB)

Momentum and Collisions

Momentum and Collisions 07-01

In an elastic collision, if the momentum is conserved,

then which of the following statements is true about

kinetic energy?

A) Kinetic energy is also conserved.

B) Kinetic energy is gained.

C) Kinetic energy is lost.

D) none of the above

Momentum and Collisions

Momentum and Collisions 07-01

When is kinetic energy conserved?

A) in inelastic collisions

B) in any collision in which the objects do not stick together

C) in all collisions

D) in elastic collisions

Momentum and Collisions

Momentum and Collisions 07-01

When a light beach ball rolling with a speed of 6.0 m/s

collides with a heavy exercise ball at rest, the beach ball's

speed after the collision will be, approximately,

A) 0.

B) 3.0 m/s.

C) 6.0 m/s.

D) 12 m/s.

Momentum and Collisions

Momentum and CollisionsProblem

Two billiard balls of equal mass undergo a perfectly elastic head-on collision. If one ball’s initial speed was 2.00 m/s and the other’s was 3.00 m/s in the opposite direction, what will be their speeds after the collision?

Momentum and Collisions

Collisions

h

v

Cons. Energy

Cons. Momentum

Ballistic Pendulum

vo

M

m

Momentum and Collisions

Collisions

h

Cons. Momentum

V

Ballistic Pendulum

Find the speed

of the bullet

v

M

m

Momentum and Collisions

Collisions

h

Cons. Energy

V

Ballistic Pendulum

M

Momentum and Collisions

Momentum and CollisionsProblem

A 28 g rifle bullet traveling 230 m/s buries itself in a 3.6 kg pendulum hanging on a 2.8 m long string, which makes the pendulum swing upward in an arc. Determine the vertical and horizontal components of the pendulum’s displacement.

Momentum and Collisions

Momentum and CollisionsProblem

A bullet is fired vertically into a 1.40 kg block of wood at rest directly above it. If the bullet has a mass of 29.0 g and a speed of 510 m/s how high will the block rise after the bullet becomes embedded in it?

Momentum and Collisions

Momentum and Collisions 07-01

Two objects collide and bounce off each other.

Linear momentum

A) is definitely conserved.

B) is definitely not conserved.

C) is conserved only if the collision is elastic.

D) is conserved only if the environment is frictionless.

Momentum and Collisions

Momentum and Collisions 07-01

A 100 kg football linebacker moving at 2.0 m/s tackles

head-on an 80 kg halfback running 3.0 m/s. Neglecting

the effects due to digging in of cleats,

A) the linebacker will drive the halfback backward.

B) the halfback will drive the linebacker backward.

C) neither player will drive the other backward.

D) this is a simple example of an elastic collision.

Momentum and Collisions

Center of Mass (cm)

xcm

y

m2

m1

x

cm

x1

x2

Momentum and Collisions

Center of Mass (cm)

xcm

Rm

Location of the cm of the Earth-Moon system

mm

me

x

Momentum and Collisions

Momentum and CollisionsProblem

y

x

Find the center of mass of the three-mass system shown in the diagram. Specify relative to the left-hand 1.00 kg mass.

1.0 kg 1.5 kg 1.1 kg

0.5 m 0.25 m

Momentum and Collisions

Momentum and Collisions 07-01

Consider two unequal masses, M and m. Which of the

following statements is false?

A) The center of mass lies on the line joining the

centers of each mass.

B) The center of mass is closer to the larger mass.

C) It is possible for the center of mass to lie within

one of the objects.

D) If a uniform rod of mass m were to join the two masses,

this would not alter the position of the center of mass of

the system without the rod present.

Momentum and Collisions

Momentum and Collisions 07-01

Two cars collide head-on on a level friction-free road.

The collision was completely inelastic and both cars

quickly came to rest during the collision. What is true

about the velocity of this system's center of mass?

A) It was always zero.

B) It was never zero.

C) It was not zero, but ended up zero.

D) none of the above

Momentum and Collisions

Chapter 7 Summary

Momentum :

Impules:

Newton’s second law:

Total momentum of an isolated system of objects is conserved.

Momentum is conserved during collisions.

Momentum and Collisions

Chapter 7 Summary

In an elastic collision, total kinetic energy is also conserved

In an inelastic collision, some kinetic energy is lost.

In a completely inelastic collision, the two objects stick together after the collision.

The center of mass of a system is the point at which external forces can be considered to act.

Momentum and Collisions

END